Unit 4 Congruent Triangles Homework 6 Answer Key (2024)

FAQs

What makes triangles congruent answer key? ›

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.

SSS (Side, Side, Side) SAS (Side, Angle, Side) ASA (Angle, Side, Angle) AAS (Angle, Angle, Side)

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.

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.

Correct answer:

The Side-Angle-Side Theorem (SAS) states that if two sides and the angle between those two sides of a triangle are equal to two sides and the angle between those sides of another triangle, then these two triangles are congruent.

If in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D, then triangle ABC is congruent to triangle DEF. Using words: If 3 sides in one triangle are congruent to 3 sides of a second triangle, then the triangles are congruent.

Regarding right triangles, there are four theorems that prove congruence. They are the leg-leg theorem, the hypotenuse-leg theorem, the hypotenuse-angle theorem, and the leg-angle theorem.

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.

Theorem 4: If in two triangles, the sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.

1. SSS (side, side, side) 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.

Is congruent to symbol? ›

The symbol ≡ means “is congruent to”. Two triangles are similar if they have the same shape.

Congruent: Two angles are called congruent angles if they have the exact same measure. It does not matter if the angles are facing different directions or if the rays forming the angles are different lengths - all that matters is the measure of the angles in degrees.

Definition of Congruent Triangles. Two triangles are congruent if all corresponding angles are congruent and all corresponding sides are congruent.

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.

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles.