Isosceles Equilateral and Congruent Triangles

Classify the triangle by its sides: 2cm, 2cm, 2cm

Classify the triangle by its sides: 7ft, 11ft, 7ft

Classify the triangle by its sides: 9m, 8m, 10m

For isosceles triangles, when we are given that two sides are congruent we can prove that ______________________.

$$In\ \Delta DEF,\ \overline{DE\ }\approx\overline{DF}.\$$  Use the base angles theorem to choose the two congruent angles.

Complete the statement.

$$If\ \overline{HG}\approx\overline{HK},\ then\ \angle HGK\ \approx\angle\ldots$$  

Complete the statement.  $$If\ \angle KHJ\approx\angle KJH,\ then\ \overline{KH}\approx\ldots$$  

Use the triangle sum theorem and the base angles theorem to find a.

Find the measure of the missing side.

$$Find\ m\angle P.$$  

Find the value of x and y.

What is the measure of BC?

Solve for x.

Find the value of x. (Hint: What type of triangle is this?)

Find the value of y.

Find the value of x.

Find the value of x. (Hint: what kind of triangle is this?)

Find the value of y.

Triangle KLM is equilateral with KM = x + 2, LM = 12 – x, and KL = 4x – 13.

Find the value of x.

(Hint: draw a picture)