Download Congruence vs. Similarity

Congruence vs. Similarity
Name:____________________
1. Congruent means what two things?
a. ______________________________
b. ______________________________
2. You have already worked with proving triangles congruent in several situations (SAS,
SSS, ASA, AAS). What does the A and S stand for?
a. ______________________________
b. ______________________________
3. Today we will be working with proving triangles similar, not proving triangles
congruent. What does it mean for two triangles to be similar?
4. What is the difference between proving triangles congruent and proving triangles
similar?
5. Draw a small triangle that has one 50° angle and one 60° angle. Label the 50° angle
with a capital N. Label the 60° angle with a capital A. Label the third angle with a
capital P.
Congruence vs. Similarity
Name:____________________
6. Now draw a larger triangle that has one 50° angle and one 60° angle. Label the 50°
angle with a capital T. Label the 60° angle with a capital I. Label the third angle with
a capital M.
7. Using a ruler, measure the sides to the nearest millimeter and write below.
NA = _______
TI = ________
AP = _______
IM = ________
PN = _______
MT = ________
8. Write your measurements as a ratio. Use the examples below and plug in.
=
=
=
9. What conclusions can you make about your two triangles?
10. Complete this conjecture. If two angles of a triangle are congruent to two
corresponding angles of another triangle, then the two triangles are
______________________.
The ratio you found on problem number 8 is called a scale factor. You can find the scale
factor of similar shapes by writing a ratio and reducing it. But, you have to match up the sides
and angles first.
Congruence vs. Similarity
Name:____________________
11. Match up the corresponding angles and sides of the given similar quadrilaterals from
bigger to smaller.
12. Now, that we know how they match up, use the given side lengths to write a
proportion and solve for y.
13. Can you solve for y and z now too?
14. Can you find the perimeter of both quadrilaterals?
Congruence vs. Similarity
Name:____________________
15. What is the ratio of the perimeters from bigger to smaller?
16. What is the ratio of ?
17. What is the scale factor?
18. When two polygons are similar we use the symbol instead of . How could you write a
statement about these two similar quadrilaterals?
19. Find the scale factor of the smaller figure to the larger figure.
20. Are the polygons similar, yes or no? Show work.