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.

Two triangles are similar if they have the same shape but not necessarily the same size. The corresponding angles are equal, and the corresponding sides are proportional. We can think of one similar triangle as an enlargement or a reduction of the other.

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.

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.

SSS (Side-Side-Side)

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule. In the above-given figure, AB= PQ, BC = QR and AC=PR, hence Δ ABC ≅ Δ PQR.

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.

SSS stands for “side, side, side” and means that we have two triangles with all three sides equal. If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.

What is the congruence rule? ›

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.

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.

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.

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.