Congruent Triangles Coloring Activity Dinosaur Answer Key (2024)

FAQs

What makes triangles congruent answer key? ›

Two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

When triangles are congruent, six facts are always true. Corresponding sides are congruent. Corresponding angles are congruent. The good news is that when trying to verify that two triangles congruent , it is not necessary to show that all six of these facts to be true.

The SAS postulate claims that triangles are congruent if two sides and one angle (between the sides) of one triangle are equal to two sides and one angle of another triangle. Finally, the SSS postulate claims that triangles are congruent if the three sides of one are equal to the three sides of another one.

ASA: If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. SAS: If any two angles and the included side are the same in both triangles, then the triangles are congruent.

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal.

Conditions for Congruence of Triangles:

SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side) RHS (Right angle-Hypotenuse-Side)

Two triangles are congruent if they satisfy the 5 conditions of congruence. They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS) and right angle-hypotenuse-side (RHS).

For example, they can use the congruence of triangles to ensure that the sleeve of a shirt is the correct length, or that a skirt is the right size. If two triangles have the same angles and side lengths, then the clothing item will fit well.

What's so great about triangle congruence criteria? Two figures are congruent if and only if we can map one onto the other using rigid transformations. Since rigid transformations preserve distance and angle measure, all corresponding sides and angles are congruent.

An included angle is the angle between two sides of a triangle. It can be any angle of the triangle, depending on its purpose. The included angle is used in proofs of geometric theorems dealing with congruent triangles. Congruent triangles are two triangles whose sides and angles are equal to each other.

What are the five theorems that prove triangle congruence? ›

What are the 5 ways to prove triangles congruent? There are five theorems that can be used to show that two triangles are congruent: the Side-Side-Side (SSS) theorem, the Side-Angle-Side (SAS) theorem, the Angle-Angle-Side (AAS) theorem, the Angle-Side-Angle (ASA) theorem, and the Hypotenuse-Leg (HL) theorem.

Notation. A symbol commonly used for congruence is an equals symbol with a tilde above it, ≅, corresponding to the Unicode character 'approximately equal to' (U+2245).

Two triangles are congruent if they have three equal length sides and three equal angles.

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. If ∠A ≅ ∠D, ∠C ≅ ∠F, and — BC ≅ — EF , then △ABC ≅ △DEF.

There are five theorems that can be used to show that two triangles are congruent: the Side-Side-Side (SSS) theorem, the Side-Angle-Side (SAS) theorem, the Angle-Angle-Side (AAS) theorem, the Angle-Side-Angle (ASA) theorem, and the Hypotenuse-Leg (HL) theorem.