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Unit 1 - Lesson 10 - Grade 8: Illustrative Mathematics

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Last updated 2 months ago
18 Questions
Note from the author:
Grade 8 Unit 1
Lesson 10: Composing Figures
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 1
Lesson 10: Composing Figures
CC BY 2021 Illustrative Mathematics®
Lesson: Composing Figures

Angles of an Isosceles Triangle (Warm Up)

Here is a triangle.
1.

Reflect triangle ABC over line AB. Label the image of C as C'.

2.

Rotate triangle ABC' around A so that C'
matches up with B.

3.

What can you say about the measures of angles B and C?

Triangle Plus One

Here is triangle ABC.
4.

Draw midpoint M of side AC.

5.

Rotate triangle ABC 180 degrees using
center M to form triangle CDA. Draw and label this triangle.

6.

What kind of quadrilateral is ABCD?
Explain how you know.

Triangle Plus Two

The picture shows 3 triangles. Triangle 2 and Triangle 3 are images of Triangle 1 under rigid transformations.
7.

Describe a rigid transformation that takes Triangle 1 to Triangle 2. What points in Triangle 2 correspond to points A, B, and C in the original triangle?

8.

Describe a rigid transformation that takes Triangle 1 to Triangle 3. What points in Triangle 3 correspond to points A, B, and C in the original triangle?

9.

Find two pairs of line segments in the diagram that are the same length, and explain how you know they are the same length.

10.

Find two pairs of angles in the diagram that have the same measure, and explain how you know they have the same measure.

Triangle ONE Plus (Optional)

Here is isosceles triangle ONE. Its sides ON and have OE equal lengths. Angle O is 30 degrees. The length of ON is 5 units.
11.

Reflect triangle ONE across segment ON. Label the new vertex M.

12.

What is the measure of angle MON?

13.

What is the measure of angle MOE?

14.

Reflect triangle MON across segment OM. Label the point that corresponds to N as T.

15.

How long is...


How do you know?


16.

What is the measure of angle TOE?

17.

If you continue to reflect each new triangle this way to make a pattern, what will the pattern look like?

Cool Down: Identifying Side Lengths and Angle Measures

Identifying Side Lengths and Angle Measures

Here is a diagram showing triangle ABC and some transformations of triangle ABC.

On the left side of the diagram, triangle ABC has been reflected across line AC to form quadrilateral ABCD. On the right side of the diagram, triangle ABC has been rotated 180 degrees using midpoint M as a center to form quadrilateral ABCE.
18.

Using what you know about rigid transformations, side lengths and angle measures, label as many side lengths and angle measures as you can in quadrilaterals ABCD and ABCE.