CPM, Lesson 1.2.4, 1-84
FACTS ABOUT ISOSCELES TRIANGLES
How can transformations such as reflections help us to learn more about familiar shapes? Consider reflecting a line segment (the portion of a line between two points) across a line that passes through one of its endpoints. An example of this would be reflecting across line in the picture below. 
Complete prompts A and B in the GeoGebra applet below.
Part A. Construct segment and line by using the segment 
and line 
tools. Then create , the reflection of , using the reflection tool 
. Connect points A and A' with the segment tool. What figure is formed by points A, B, and A'?
Note: Point B might be covered by point B'
Part B. Use what you know about reflections to make as many statements as you can about the shape formed in part (A). For example, are there any sides that must be the same length? Are there any angles that must be equal? Is there anything else special about this shape? Consider using the angle 
and distance 
measurement tools to conduct your investigation.
and line tools. Then create , the reflection of , using the reflection tool . Connect points A and A' with the segment tool. What figure is formed by points A, B, and A'?
Note: Point B might be covered by point B'
Part B. Use what you know about reflections to make as many statements as you can about the shape formed in part (A). For example, are there any sides that must be the same length? Are there any angles that must be equal? Is there anything else special about this shape? Consider using the angle and distance measurement tools to conduct your investigation. LEARNING LOG
When two sides of a triangle have the same length, that triangle is called isosceles. In your Learning Log, describe all the facts you know about isosceles triangles based on the reflection. Refer to your construction and exploration above.