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.

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. : Two pairs of corresponding angles and the corresponding sides between them are equal.

SAS Congruence Rule (Side – Angle – Side)

Two triangles are said to be congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle. Proof : In the given figure OA = OB and OD = OC.

Congruence of triangles: Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.

You have to measure the length of both triangles separately, like AB, BC, and AC, and XY, YZ, and ZX. You also need to measure the angle between triangles XYZ and PQR. If you find AB=XY, BC=YZ, and the angles of both triangles equal to each other, then you have proven a congruent triangle with SAS.

Side Side Side Congruence Theorem

Side-Side-Side (SSS) congruence theorem states that if three sides of a triangle is equal to the corresponding sides of the other triangle, the two triangles are said to be congruent. Let us see the proof of the theorem: Given: AB = DE, BC = EF, and AC = DF. To prove: ∆ABC ≅ ∆DEF.

If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Triangles that have exactly the same size and shape are called congruent triangles. The symbol for congruent is ≅. Two triangles are congruent when the three sides and the three angles of one triangle have the same measurements as three sides and three angles of another triangle.

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).

SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.

Can you use AA to prove triangle congruence? ›

Angle-Side-Angle Postulate and Angle-Angle-Side Theorem

Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side in one triangle are congruent to two angles and the corresponding non-included side in another triangle, then the triangles are congruent.

The ASA Theorem (angle-side-angle) says that if two angles and the side between them of one triangle are congruent to two angles and the side between of another triangle, then the triangles are congruent. There is no need to check the value of the third angle or the other two sides.

SAS criterion is true when In two triangles, a pair of corresponding sides are proportional and the included angles are equal then the two triangles are similar.

Equilateral triangles have interior angles that are all congruent so they are equiangular.

SSS refers to the equality of three sides between triangles. AAS refers to the equality between two sides and an angle between triangles. SAS refers to the equality between two sides and an angle (between the sides) between triangles. ASA refers to the equality between two angles and one side between triangles.

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled triangle.

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.