Contents

- 1 What is an example of congruent in math?
- 2 How do you know if its congruent?
- 3 Is congruent different than equal?
- 4 What’s another word for congruent?
- 5 Does congruent mean same size?
- 6 Which is always congruent?
- 7 What does congruent look like?
- 8 How do you know if something is not congruent?
- 9 What shape is not congruent?
- 10 What is a real example of congruent shapes?

## What is an example of congruent in math?

Congruent Line Segments – Since congruence implies equal shape and size, the line segments will be congruent if their shape and size is the same. Observe the above image carefully. Since both AB and PQ are line segments they are of the same shape. The length of line segment AB is equal to 5 cm and PQ is also equal to 5 cm.

### Does congruent mean equal sides?

Two segments are congruent if and only if they have equal measures. Two triangles are congruent if and only if all corresponding angles and sides are congruent.

#### What does congruent mean simple?

: having the same size and shape : capable of being placed over another figure and exactly matching. congruent triangles. congruently adverb.

### Does congruent mean 90?

Are Right Angles Congruent? – Right angles are always congruent as their measurement is the same. They always measure 90°.

## How do you know if its congruent?

Two triangles are said to be congruent if their sides have the same length and angles have same measure. Thus, two triangles can be superimposed side to side and angle to angle. In the above figure, Δ ABC and Δ PQR are congruent triangles.

#### How do you know something is congruent?

Congruent shapes Here we will learn about congruent shapes, including what they are and how to recognise them. There are also congruent shapes worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck. The red shape has been translated to give the blue shape.E.g. These two quadrilaterals are congruent. The red shape has been reflected to give the blue shape.E.g. These two polygons are congruent. The red shape has been rotated to give the blue shape.E.g. These two polygons are NOT congruent. They are similar. The red shape has been enlarged by multiplying by a scale factor to give the blue shape. If two shapes are the same but different sizes, one being an enlargement of the other, these are known as similar shapes.

- There are four conditions to be able to prove if a pair of triangles are congruent.
- Reasons for congruency:
- SSS (three sides the same),
- RHS (right-angled triangle, hypotenuse and a side the same),
- ASA or AAS (two angles and one side the same),
- SAS (side-angle-side, two sides and the included angle the same).

E.g. These two triangles are congruent triangles.

- They have two angles that are the same.
- The side in between the angles is also equal.
- The congruence condition would be angle-side-angle (which is abbreviated to ASA).

In order to recognise congruent shapes:

- Check the type of 2D shape.
- Check the corresponding angles and corresponding sides.
- State if the shapes are congruent or not.

Get your free congruent shapes worksheet of 20+ questions and answers. Includes reasoning and applied questions. x Get your free congruent shapes worksheet of 20+ questions and answers. Includes reasoning and applied questions. Congruent shapes is part of our series of lessons to support revision on congruence and similarity,

Are these 2D shapes congruent?

Check the type of 2D shape.

- Both shapes are rectangles.
- 2 Check the corresponding angles and corresponding sides.
- All the angles are 90^,
- The short sides on both rectangles are 1.
- The long sides on both rectangles are 3.

3 State if the shapes are congruent or not, The shapes are the shape shape and the same size – they are congruent shapes. Are these 2D shapes congruent? Check the type of 2D shape. Both shapes are rectangles. Check the corresponding angles and corresponding sides.

- All the angles are 90^,
- The short sides on both rectangles are 2.
- The long sides on both rectangles are different.

State if the shapes are congruent or not. The shapes are both rectangles but – they are NOT congruent shapes. Are these 2D shapes congruent? Check the type of 2D shape. Both shapes are trapeziums. Check the corresponding angles and corresponding sides.

- The angles are 90^, 45^ and 135 ^,
- They are in corresponding positions.
- The lengths of the corresponding sides are different lengths.
- The side lengths of the second shape are double the lengths of the first shape.

State if the shapes are congruent or not. The shapes are the same shape, but different sizes. They are similar shapes but – they are NOT congruent shapes. Are these 2D shapes congruent? Check the type of 2D shape. One shape looks like a capital letter “C” and the other shape looks like a capital letter “L”. Check the corresponding angles and corresponding sides.

- There are lots of right angles in both shapes.
- There are lots of sides of length 1 and 3,
- But they are not in corresponding positions as the shapes are different shapes.

State if the shapes are congruent or not. The shapes are different shapes. They are NOT congruent shapes. Are these 2D shapes congruent? Check the type of 2D shape. It can be tricky to see if these shapes are the same type of 2D shape. They both have 6 sides so they are irregular hexagons.

Check the corresponding angles and corresponding sides. The angles are 90^, 225^ and 135^, They are in corresponding positions as you go the same direction around the shapes. Looking at the side lengths – they are in corresponding positions as you go round the shapes in the same direction. State if the shapes are congruent or not.

The shapes are the same shape and the same size. A rotation is involved. They are congruent shapes. Are these 2D shapes congruent? Check the type of 2D shape. It can be tricky to see if these shapes are the same type of 2D shape. They both have 6 sides so they are irregular hexagons.

- Check the corresponding angles and corresponding sides.
- There are 4 right angles in both shapes.
- The two other angles are equal and are in corresponding positions as you go round the shapes.
- But one in clockwise direction, one in an anticlockwise direction.
- Looking at the side lengths there are lots of sides of length 1 and 3 and a diagonal.

They are in corresponding positions as you go round the shapes. But one in clockwise direction, one in an anticlockwise direction. State if the shapes are congruent or not. The shapes are the same shape and the same size. A rotation and a mirror image is involved.

Shapes can be congruent but in different orientations

The second shape may be in a different orientation to the first shape. The shapes can still be congruent. Perhaps use tracing paper to help you check.

Shapes can be congruent but mirror images

The second shape may be a mirror image of the first shape. The shapes can still be congruent. Perhaps use tracing paper to help you check.

Use the grid lines to help you compare shapes

Some shapes on a grid can be tricky. Use the straight lines on the grid to help you identify right angles and work out the side lengths. Be careful with the diagonals.

In most diagrams the diagrams are NOT drawn to scale

Questions about congruent shapes are often on grids. But sometimes diagrams may have shapes which are NOT drawn to scale. So use the measurements given, rather than measuring for yourself. The original shape is a rectangle with sides 1 and 4, So has shape C.

Shape A is the same as the original shape, but has been rotated. The original shape is a rectangle with sides 3 and 4. So has shape D. Shape B is the same as the original shape, but is upside down. Shape C is the same as the original shape, but is a reflection. Shape C is the same as the original shape.1.

Which shape is congruent to shape X? (1 mark) 2. Which shape is congruent to shape A? (1 mark) 3. Which shape is congruent to shape M? (1 mark) You have now learned how to:

- What congruent shapes are
- How to identify congruent shapes

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## Is congruent different than equal?

If two segments have equal length, then they are congruent. It is informal to say that two figures are equal. Two figures are not equal, they are congruent if the coreesponding measurements are equal.

#### Are two sides congruent?

What are Congruent Sides? In geometry, two sides are said to be congruent if they have the same length. For example, a square has four congruent sides, because it has four sides of the same length.

## What’s another word for congruent?

Synonyms of congruent (adj. coinciding. compatible. concurring. conforming. consistent.

### Are all lines congruent?

In order to construct congruent segments, there needs to be a method to measure the line segments. This can be done by using a ruler or a compass (as in a mathematical compass used to draw circles). If a line segment is already given, a second line segment can be created using the ruler or compass method. Constructing congruent segments using a ruler:

Measure the length of the given line segment Using the straight edge of the ruler, put a dot on the paper at the ‘0’ tick on the ruler, label this dot (for example, label it as ‘A’) Continue using the straight edge of the ruler, put a dot on the paper at the tick mark indicating the length of the original line segment, and label this dot (for example, label it as ‘B’) Using the straight edge of the ruler, draw a line between the two dots

Constructing congruent segments using a compass In math, congruent line segments are often used to indicate that two shapes are similar or different. For example, take a look at these two triangles: In these two triangles, the tick marks indicate that line segment AB is congruent to line segment DE, so they are the same length. Now let’s take a look at this rectangle: In this rectangle, notice that lines AD and BC only have one tick mark each, while lines AB and DC have two tick marks each. This tells us that line AB is congruent to line DC and line AD is congruent to line BC. A line segment is a line with a definite end and beginning point.

#### Are congruent always equal?

Congruence deals with shapes (aka objects), while equality deals with numbers. You don’t say that two shapes are equal or two numbers are congruent. Two shapes are said to be congruent if one can be exactly superimposed on the other. ‘Congruence deals with shapes (aka objects), while equality deals with numbers.

### What makes a number congruent?

Congruent number Triangle with the area 6, a congruent number. In, a congruent number is a positive that is the area of a with three sides. A more general definition includes all positive rational numbers with this property. The sequence of (integer) congruent numbers starts with 5, 6, 7, 13, 14, 15, 20, 21, 22, 23, 24, 28, 29, 30, 31, 34, 37, 38, 39, 41, 45, 46, 47, 52, 53, 54, 55, 56, 60, 61, 62, 63, 65, 69, 70, 71, 77, 78, 79, 80, 84, 85, 86, 87, 88, 92, 93, 94, 95, 96, 101, 102, 103, 109, 110, 111, 112, 116, 117, 118, 119, 120,,

Congruent number table: n ≤ 120—: non-Congruent number C: square-free Congruent number S: Congruent number with square factorn | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

— | — | — | — | C | C | C | — | |

n | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

— | — | — | — | C | C | C | — | |

n | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |

— | — | — | S | C | C | C | S | |

n | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |

— | — | — | S | C | C | C | — | |

n | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |

— | C | — | — | C | C | C | — | |

n | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 |

C | — | — | — | S | C | C | — | |

n | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 |

— | — | — | S | C | S | C | S | |

n | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 |

— | — | — | S | C | C | S | — | |

n | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 |

C | — | — | — | C | C | C | — | |

n | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |

— | — | — | — | C | C | C | S | |

n | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 |

— | — | — | S | C | C | C | S | |

n | 89 | 90 | 91 | 92 | 93 | 94 | 95 | 96 |

— | — | — | S | C | C | C | S | |

n | 97 | 98 | 99 | 100 | 101 | 102 | 103 | 104 |

— | — | — | — | C | C | C | — | |

n | 105 | 106 | 107 | 108 | 109 | 110 | 111 | 112 |

— | — | — | — | C | C | C | S | |

n | 113 | 114 | 115 | 116 | 117 | 118 | 119 | 120 |

— | — | — | S | S | C | C | S |

For example, 5 is a congruent number because it is the area of a (20/3, 3/2, 41/6) triangle. Similarly, 6 is a congruent number because it is the area of a (3,4,5) triangle.3 and 4 are not congruent numbers. If q is a congruent number then s 2 q is also a congruent number for any natural number s (just by multiplying each side of the triangle by s ), and vice versa., where Q ∗ ^ } is the set of nonzero rational numbers. Every residue class in this group contains exactly one, and it is common, therefore, only to consider square-free positive integers, when speaking about congruent numbers.

## Does congruent mean same size?

Congruent Congruent Initial Definition Two figures are congruent if they have the same shape and size. Two angles are congruent if they have the same measure. Two figures are similar if they have the same shape but not necessarily the same size. Example One All of the figures below are congruent since they all have the same shape and size.

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- Example Two The figures below are NOT congruent.
- Although they are the same shape, they are different sizes.
- Figures that are the same shape but different in size are similar.
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Please try another device or upgrade your browser. Example Three The two figures below are NOT congruent since they do not have the same shape.

## Which is always congruent?

Angles and parallel lines (Pre-Algebra, Introducing geometry) – Mathplanet When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Vertical angles are always congruent, which means that they are equal. Adjacent angles are angles that come out of the same vertex. Adjacent angles share a common ray and do not overlap. The size of the angle xzy in the picture above is the sum of the angles A and B. Two angles are said to be complementary when the sum of the two angles is 90°. Two angles are said to be supplementary when the sum of the two angles is 180°. If we have two parallel lines and have a third line that crosses them as in the ficture below – the crossing line is called a transversal When a transversal intersects with two parallel lines eight angles are produced. The eight angles will together form four pairs of corresponding angles. Angles 1 and 5 constitutes one of the pairs. Corresponding angles are congruent. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g.3 + 7, 4 + 8 and 2 + 6.

Angles that are in the area between the parallel lines like angle 2 and 8 above are called interior angles whereas the angles that are on the outside of the two parallel lines like 1 and 6 are called exterior angles. Angles that are on the opposite sides of the transversal are called alternate angles e.g.1 + 8.

All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent. Example The picture above shows two parallel lines with a transversal. The angle 6 is 65°. Is there any other angle that also measures 65°?

6 and 8 are vertical angles and are thus congruent which means angle 8 is also 65°.6 and 2 are corresponding angles and are thus congruent which means angle 2 is 65°.6 and 4 are alternate exterior angles and thus congruent which means angle 4 is 65°.

## What does congruent look like?

Similar TrianglesSo what is the difference between similar and congruent? While all congruent shapes are also similar, all similar shapes are not congruent. Shapes are both congruent and similar when they have the same shape and the same size. One could be placed right over the other (known as being “superimposed”) and they would be identical – same angles, same side lengths, same shape.

Top shapes are similar. Bottom shapes are congruent.In geometry, objects and shapes are often described using the terms “similar” and “congruent” when comparing them to other objects and shapes. When something is described as similar to another object or shape, it means that the two objects are the same shape and have proportional corresponding sides.

It shows that the two shapes appear to be like each other, but not exactly the same. For example, two triangles whose corresponding sides and angles are proportional would be considered similar. If they look like they’re the same shape, just different sizes, they are said to be similar. When they are also congruent, they are not only the same shape, but also the same size.

The lengths of each of the sides and the angles between them are the same as the respective sides and angles of the other shape. Congruent shapes are always similar, but similar shapes are not always congruent. Knowing whether or not shapes are similar and/or congruent allows the student to draw different conclusions.

If the shapes are congruent, it is already known that the angles and lengths will all be the same. If the shapes are only similar, the student can determine the length of an unknown side using proportions. Recognizing these terms helps students know how to find the lengths of missing sides or the degrees of the unknown angle.

In summary, congruent shapes are those that have the same shape and the same size. Similar shapes have the same angles and proportional sides, but are different sizes.

## How do you know if something is not congruent?

Congruent shapes are the same size and shape. Rigid transformations, like translations, keep shapes congruent, but dilations are not rigid transformations because they change the size. So, if we use a dilation to map one shape onto another, they are not congruent.

#### What is congruence rule?

ASA Congruence Rule ( Angle – Side – Angle ) – Two triangles are said to be congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle. Proof : From the given two triangles, ABC and DEF in which: ∠B = ∠E, and ∠C = ∠F and the BC = EF To prove that ∆ ABC ≅ ∆ DEF For proving congruence of the two triangles, the three cases involved are Case (i): Let AB = DE You will observe that AB = DE (Assumed) Given ∠B = ∠E and BC = EF So, from SAS Rule we get, ∆ ABC ≅ ∆ DEF Case (ii): Let it possible the side AB > DE. Now take a point P on AB such that it becomes PB = DE. Now consider ∆ PBC and ∆ DEF, IT is noted that in triangle PBC and triangle DEF, From construction, PB = DE Given,∠ B = ∠ E BC = EF So, we conclude that, from the SAS congruence axiom ∆ PBC ≅ ∆ DEF Since the triangles are congruent, their corresponding parts of the triangles are also equal. So, ∠PCB = ∠DFE But, we are provided with that ∠ACB = ∠DFE So, we can say ∠ACB = ∠PCB Is this condition possible? This condition is possible only if P coincides with A or when BA = ED So, ∆ ABC ≅ ∆ DEF (From SAS axiom) Case (iii): If AB < DE, we can take a point M on DE such that it becomes ME = AB and repeating the arguments as given in Case (ii), we can conclude that AB = DE and so we get ∆ ABC ≅ ∆ DEF. Suppose now consider that in two triangles, two pairs of angles and one pair of corresponding sides are equal but the side of a triangle is not included between the corresponding equal pairs of angles. Can you say that the triangles still congruent? Absolutely, You will notice that they are congruent. Because the sum of the three angles of a triangle is 180°. If two pairs of angles are equal, the third pair of angles are also equal. It is called as AAS congruence rule when two triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal.

## What shape is not congruent?

Plane shapes which have the same shape and are the same size are called congruent. For shapes to be congruent they must satisfy both the following conditions:

matching (or corresponding) angles are equal matching (or corresponding) sides are equal in length.

These two shapes have matching angles equal but their matching sides are not equal and so they are not congruent. They are the same shape but not the same size. Non-congruent rectangles. These two polygons have matching sides equal but their matching angles are not equal and so they are not congruent. They are different shapes even though the sides are the same size. Non-congruent hexagons. Congruent shapes can be superimposed on each other by rotation, translation or reflection (or a combination of these transformations). All of these quadrilaterals are congruent. Congruence can be a feature of any type of plane shape. Explore the link between congruent shapes and transformations further. There are special conditions for congruent triangles.

## What is a real example of congruent shapes?

Solution: When one shape is placed over the other and if they superimpose one over the other, they are said to be congruent. Two figures are congruent if they have the same shape and size. Two real-life examples of congruent shapes are: 1) Two mobile phones of the same model of the same brand.2) Two NCERT mathematics textbooks of class VII.

☛ Check: NCERT Solutions for Class 7 Maths Chapter 7 Video Solution: NCERT Solutions for Class 7 Maths Chapter 7 Exercise 7.1 Question 2 Summary: Two real-life examples for congruent shapes are: 1) Two mobile phones of the same model of the same brand, 2) Two NCERT mathematics textbooks of class VII.

☛ Related Questions:

Complete The Following Statements A Two Line Segments Are Congruent If B Among The Congruent Angles One Has A Measure Of 70 The Measure Of The Other Angle Is If Abc Fed Under The Correspondence Abc Fed Write All The Corresponding Congruent Parts Of The Triangles If Def Bca Write The Part Of Bca That Correspond To I E Ii Ef Iii F Iv Df Which Congruence Criterion Do You Use In The Following A Given Ac Df Ab De Bc Ef So Abc Def B Given Zx Rp Rq Zy Prq Xzy So Pqr Xyz

### What does congruent look like?

Similar TrianglesSo what is the difference between similar and congruent? While all congruent shapes are also similar, all similar shapes are not congruent. Shapes are both congruent and similar when they have the same shape and the same size. One could be placed right over the other (known as being “superimposed”) and they would be identical – same angles, same side lengths, same shape.

Top shapes are similar. Bottom shapes are congruent.In geometry, objects and shapes are often described using the terms “similar” and “congruent” when comparing them to other objects and shapes. When something is described as similar to another object or shape, it means that the two objects are the same shape and have proportional corresponding sides.

- It shows that the two shapes appear to be like each other, but not exactly the same.
- For example, two triangles whose corresponding sides and angles are proportional would be considered similar.
- If they look like they’re the same shape, just different sizes, they are said to be similar.
- When they are also congruent, they are not only the same shape, but also the same size.

The lengths of each of the sides and the angles between them are the same as the respective sides and angles of the other shape. Congruent shapes are always similar, but similar shapes are not always congruent. Knowing whether or not shapes are similar and/or congruent allows the student to draw different conclusions.

- If the shapes are congruent, it is already known that the angles and lengths will all be the same.
- If the shapes are only similar, the student can determine the length of an unknown side using proportions.
- Recognizing these terms helps students know how to find the lengths of missing sides or the degrees of the unknown angle.

In summary, congruent shapes are those that have the same shape and the same size. Similar shapes have the same angles and proportional sides, but are different sizes.

### What is an example of a congruent sides?

What are Congruent Sides? In geometry, two sides are said to be congruent if they have the same length. For example, a square has four congruent sides, because it has four sides of the same length.