Download Corresponding Sides and Angles of Similar Triangles

Project AMP
Dr. Antonio Quesada – Director, Project AMP
Corresponding Sides and Angles of Similar Triangles
Lesson Summary:
Students will construct two similar triangles using Geometry software and
discover the relationships between the angles and the sides of the two triangles.
Key Words:
similar triangles
Background Knowledge:
Students should be familiar with the Geometry software.
Learning Objectives:
Students will determine the relationships between the corresponding sides and
angles of two similar triangles.
Materials:
Geometry software
Suggested Procedure:
Split students into groups of two or three. Have students complete the
worksheets.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Corresponding Sides and Angles of Similar Triangles
Group member’s names: __________________________________________________
File name: ______________________________________________________________
Goal: Construct two similar triangles between three rays and determine the relationship
of the angles and the sides of these triangles.
Perform the following tasks using Geometry Software.
1. Make a point on the left side of your screen and label this point ‘P’. [Use point tool]
2. Construct three rays that extend to the right of point P. [Use ray tool]
3. Construct ∆ ABC so that each point of the triangle lies on a
different ray. Put point A on the center ray, point B on the
top ray and point C on the bottom ray. Make sure you label
each point. [Use triangle and label tools]
4. Make a point ‘X’ on the center ray PA to the right of ∆ ABC. Construct a line
parallel to side AB through point X and a line parallel to side AC , also through
point X. [Use point and parallel line tools]
5. Mark the intersection of ray PB and the line parallel to side
AB with point ‘Y’. Mark the intersection of ray PC and
the line parallel to side AC with the point ‘Z’. Construct a
segment YZ that goes from point ‘Y’ to point ‘Z’. [Use point,
label and segment tools]
6. Construct segment XY and segment XZ . Use the “hide/show” tool to hide line
XZ and line XY . Your figure should now consist of ∆ ABC and ∆ XYZ
between three rays that share a common vertex, point ‘P’.
[Use segment and hide/show tools]
7. Find the length of all of the segments in each triangle. [Use distance and length tool]
8. Calculate the ratio of segment AB to XY , segment BC to YZ , and segment CA
to ZX . Put these ratios in a blank section of your screen and use the comment
tool to rename each for clarity. [Use calculate and comment tools]
9. What did you find out about the ratios of the sides of these two triangles?
Project AMP
Dr. Antonio Quesada – Director, Project AMP
10. Find the measurements of all the angles in ∆ ABC and ∆ XYZ.
[Use the angle tool]
11. How are the measurements of ∠ BAC and ∠ YXZ related? How about ∠ ABC
and ∠ XYZ? … ∠ BCA and ∠ YZX?
12. What can you conclude about these two triangles? Explain how you came to your
conclusion.
Extension:
1. Create a table to capture all segment lengths, angle measures, ratios of segments,
area of each triangle and the ratio between the areas, perimeter of each triangle,
and ratio between perimeters.
2.
3.
Use pointer tool to move point X, which will move ∆ XYZ. Move point X in
both directions along ray PA , also consider moving point X in between point P
and point A.
Capture values for table entries periodically as you move point X along ray PA .
What relationships did you discover as point X was moved along ray PA ? [Use
tabulate, calculate, pointer, and comment tools]
•
If you are not familiar with Cabri’s tools, press F1. A help menu for each tool selected will appear on the screen.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Journal Activity
Corresponding Sides and Angles of Similar Triangles
1. What was your favorite thing about this activity?
2. What was the most challenging thing?
3. What did you gain the most confidence about through completing this
lesson?
4. Where do you possibly see yourself using this knowledge in the future?