Warm-Up

1. 56 ÷ (-7)

2. (-4) • 7

3. 38 – (-3)

4. -7 + 3

Essential Question

Similar and Congruent Figures

Unit 1, Day 1

Common Core GPS:

MCC8.G.1: Verify experimentally the properties of rotations, reflections, and translations:

a. Lines are taken to lines, and line segments to line segments of the same length.

b. Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines.

Language of the Standards:

Corresponding sides: sides that have the same relative positions in geometric figures.

Corresponding angles: angles that have the same relative positions in geometric figures.

Congruent figures: figures that have the same size and shape.

Similar figures: figures that have the same shape but not necessarily the same size.

Scale factor: the ratio of two corresponding lengths of the sides of two similar figures.

Scale Factor Review

What is the scale factor of the following figures? How do you know?

Scale Factor Review

What is the scale factor of the following figures? How do you know?

Scale Factor

What is the scale factor?

Scale Factor

Use scale factor to find the missing side.

Corresponding Sides and Angles

Given that ΔABC ~ΔXYZ. List the corresponding sides and angles.

What does this symbol mean?

??

So, in order to have similar figures what must be true?

Work Session:

1. Explain: The sketch below shows two triangles, ΔLMN and ΔFGE. How do you know that the triangles are similar? Is there anything else you can say about the two triangles?

2. List: Name the pairs of corresponding sides and the pairs of corresponding angles.

3. Compare: How are the corresponding sides related and how are the corresponding angles related? Why is this true?

The sketch below shows two triangles, ΔABC and ΔEFG. ΔABC has an area of 12 square units and its base (AB) is equal to 8 units. The base of ΔEFG is equal to 24 units.

4. Explain: How do you know that the triangles are similar? (Hint: Think scale factor.)

5. List: Name the pairs of corresponding sides and the pairs of corresponding angles.

6. The sketch below shows two triangles, ΔMNO and ΔQPR. How do you know that the triangles are similar?

7. Name the corresponding sides and the corresponding angles. Using the LOTS, explain how you know that the corresponding sides and angles are related.

Review:

The polygons in each pair are similar. Find the missing side length.

8. 9.

10. 11.

Closing:

Share answers and discuss as needed.