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.

From the basic concepts of triangles we know that the two triangles are said to be congruent if they are of the same shape and size whereas two triangles are said to be similar if they are of the same shape but can be of different sizes.

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.

Two triangles are congruent when they have the same shape and size such that corresponding sides and angles are equal. Corresponding parts of congruent triangles are congruent. If two angles are known in a triangle, then the third angle is also known since the sum of the angles must equal 180∘ .

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.

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.

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent. In Δ PQR and ΔXYZ, as shown below, we can identify that PQ = XY, PR = XZ, and QR = YZ and ∠P = ∠X, ∠Q = ∠Y and ∠R = ∠Z.

What are the 4 basic rules for triangle congruence? ›

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.

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.

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.