# 4.2 Isosceles Triangles

## Directions

There are 2 investigations that you need to complete to notice some relationships that are true in isosceles triangles. When you are finished, get your conjectures checked and move on to the next part of your notes.

Investigation #1: Use the polygon tool to create a triangle with vertices A, B, and C. A and B are already shown. C must be somewhere else on the arc of the circle. Change the angle measure tool to a distance tool, and measure all 3 sides of the triangle.

## Vocabulary Check

Based on the lengths of the sides of the triangle, which of the following words correctly describes ?

## Change the distance tool back to an angle measure tool. Measure all 3 angles of the triangle. Then use the arrow tool to click and drag C so that your triangle changes size.

What is always true about and ?

## C-18 Isosceles Triangle Conjecture

Choose the word that correctly completes the following sentence: If a triangle is isosceles, then its base angles are _____.

Investigation #2: AB is the base of your triangle. Change the angle measure tool to "Angle with given size" tool. Click on point B, then A, then choose an acute angle measure. Change the line tool to a ray tool, and make ray AB'.

## Next Step

Now choose the "Angle with given size" tool again. This time, click on A, then B, then click the button for "clockwise" and enter the same acute angle you did before.
Use the ray tool to make ray BA'.
Use the point tool to make a point where the rays intersect. Name it C.

Change the "Angle with given size" tool to a distance tool and measure the 3 sides of the triangle. Use the arrow tool to click and drag point A or point B to change the size of your triangle. What do you notice about AC and BC?

## C-19 Converse of the Isosceles Triangle Conjecture

Choose the word that correctly completes the sentence. If a triangle has two congruent angles, then it is a/n _______________________ triangle.