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**Geometry UNIT 7 EXAM **

Name ____________________________

Period ___________ Date ____________

Basic: 1 correct = 3 points

Proficient: 2 correct = 4 points

Advanced: 3 correct = 6 points

**Section 1: Solve the following proportions. **

B.

8

*x*

P.

3

*x*

9

3 6 4 2

**Section 2: Similar Polygons **

use the figure provided

A.

*x x*

1

2

5

B.

Write a similarity statement.

Trapezoid ___________ ~ Trapezoid ___________

P.

What is the length of ZD? (set up a proportion and solve!)

A. Solve for x. and y. (must get both correct!) x = ________ y = __________

**Section 3: Word Problems: **

set up proportions to solve!

B. If a hen lays 4 eggs in 7 days, how many eggs will there be in 35 days?

P. A woman 6ft tall casts a shadow 4ft long. At the same time, the shadow of a nearby cactus casts a shadow 18ft long. How tall is the cactus?

A. Karissa places a mirror 15 ft from the base of a tree. When she stands 2 ft from the mirror, she can see the top of the tree reflected in it. If her eyes are 5ft above the ground, how tall is the tree?

**Section 4: Triangle Similarity Theorems**

Are the triangles similar? If yes, name the THEOREM and show it’s true. If no, EXPLAIN.

P. A. B.

**Section 5: Simplifying Radicals (NO DECIMALS!) Break it down!**

B. 84 P. 16

6 A. 9

2

**Section 6: Similar Right Triangles and Geometric Mean**

B. Find the geometric mean of 9 and 25. If the answer is not a whole number, leave it in simplest radical form.

P. Solve for x. A. Solve for a and b.

**Section 7: Triangle Proportions**

B. Solve for x

B. same shape, same size

P. Solve for x.

A. The extendable ramp is used to move crates of fruit to loading docks of different heights. When the horizontal distance AB is 4 feet, the height of the loading dock, BC, is 3 feet. What is the height of loading dock DE? HINT: You may want to redraw the triangles!

**Section 8: Vocabulary**

____ Congruent A. The use of similar triangles to find distances that are difficult to measure directly.

____ Indirect Measurement

____ Means

*x*

C. In the proportion

*y*

*t z*

that part y and z

____ Similar D. Setting two ratios equal

____ Ratio

*x*

E. In the proportion

*y*

*t z*

the part x and t

____ Extremes F. 12 : 9 or

12

9

____ Proportion G. same shape, not necessarily same size