### Home > INT2 > Chapter 8 > Lesson 8.1.1 > Problem 8-13

Tromika wants to calculate the area of the isosceles triangle at right. Homework Help ✎She decides to start by drawing a height from vertex

*A*to side*BC*as shown below. Will the two smaller triangles be congruent? In other words, is ∆*ABD*≅ ∆*ACD*? Why or why not?

What is

*m*∠*DAB*?*BD*?Determine

*AD*. Show how you got your answer.Calculate the area of ∆

*ABC*.

Look at the two triangles that are created. They share a side, and the ticks marks mean the sides are equal. How could they be congruent?

Yes, they are congruent by HL≅.

If the segment (height) bisects both ∠*BAC* and segment *BC*, how can you calculate the measure of half of each?

∠*DAB* = 18°*BD* = 4

Which trig ratio can you use to determine this length?

How do you find the area of a triangle? Do you have enough information to calculate the area?