Congruency in isosceles and equilateral triangles

Learning Objectives Apply the properties of isosceles and equilateral triangles to prove congruency. Use the Isosceles Triangle Theorem and its converse in geometric proofs. Prove that the altitude to the base of an isosceles triangle is also the median and angle bisector. Apply congruence postulates (SSS, SAS, ASA, AAS) in problems specifically involving isosceles and equilateral triangles. Solve for unknown angles and side lengths in figures containing congruent isosceles or equilateral triangles. Construct logical two-column proofs involving congruent isosceles and equilateral triangles. Ever noticed how the trusses of a bridge use repeating triangles for strength? 🌉 Let's explore why these special triangles are so powerful in geometry and engineering! This tutoria...

TermDefinitionExample Isosceles TriangleA triangle with at least two congruent sides. The congruent sides are called legs, and the third side is the base.A triangle with side lengths 7 cm, 7 cm, and 10 cm. The sides of 7 cm are the legs, and the 10 cm side is the base. Equilateral TriangleA triangle with all three sides congruent. It is a special type of isosceles triangle.A triangle with side lengths 8 cm, 8 cm, and 8 cm. Vertex AngleThe angle formed by the two congruent sides (legs) of an isosceles triangle.In an isosceles triangle with sides 7, 7, 10, the vertex angle is the angle between the two 7 cm sides. Base AnglesThe two angles opposite the congruent sides of an isosceles triangle. These angles are always congruent.In an isosceles triangle with sides 7, 7, 10, the base angles are...

Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. If $\overline{AB} \cong \overline{AC}$, then $\angle C \cong \angle B$. Use this theorem to find the measure of an unknown angle when you know two sides of a triangle are equal. It's a key reason for proving angles are congruent in a proof. Converse of the Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent. If $\angle C \cong \angle B$, then $\overline{AB} \cong \overline{AC}$. Use this theorem to prove that two sides of a triangle are equal when you are given that two angles are equal. It's essential for proving a triangle is isosceles. Equilateral Triangle Corollary A t...