Congruent Triangles Coloring Activity Dinosaur Answer Key (2024)

FAQs

What makes triangles congruent answer key? ›

When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

If two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent.

Two triangles are said to be congruent if they are of the same size and same shape. Two congruent triangles have the same area and perimeter. All the sides and angles of a triangle are equal to the corresponding sides and angles of its congruent triangle.

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.

If two pairs of corresponding angles and a pair of non-included sides are congruent, then the triangles are congruent. In right triangles, if the pair of hypotenuses and one pair of legs are congruent, then the triangles are 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.

A triangle only has ‍ sides and ‍ angles. If we know ‍ distinct side measures or ‍ distinct angle measures, then we know the two triangles cannot be congruent.

Two integers a and b are said to be congruent modulo m if their difference a–b is divisible by the integer m. It is then said that a is congruent to b modulo m, and this statement is written in the symbolic form a≡b (mod m). Such a relation is called a congruence.

If two triangles have the same size and shape they are called congruent triangles. If we flip, turn or rotate one of two congruent triangles they are still congruent. If the sides of two triangles are the same then the triangles must have the same angles and therefore must be congruent.

Which triangle is congruent to ABC? ›

In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent. If in triangles ABC and DEF, angle A = angle D = right angle, AB = DE (leg), and BC = EF (hypotenuse), then triangle ABC is congruent to triangle DEF.

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.

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.