Geometry Unit 6
Summary Sheet
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
Name _______________________
Date ____________________________
Today you will review for Unit 6 test on 1/6 or 1/7
By the end of class today you will be able to successfully study for the test.
Unit 6 – Warm up 5
1. What does it mean for two polygons to be similar?
2. Give the postulate or theorem that justifies why the triangles are similar.
80
80
3. You want to prove that ABC PXQ using the SSS similarity theorem. Complete the
proportion that is needed to use this theorem.
AC

XQ

AB
Find the value of x.
4.
5.
x
14
x
7
7
4
18
6
6.
7
2
x
3
Ratios Proportions and Geometric Means
a) ratio
b) simplify ratio –
c)
____________ in same ______________ as given _________________
Extend Ratio of measures of angles in a triangle
1. Given the extended ratio of 2:3:5 for measures of angles in a triangle. What
are the measures for each angle?
2. NOTE: extended ratio can apply to sides. Given the ratios, solve for x.
C
BC : AC : AB = 2 : 5 : 8
2x + 6
2x
B
8x
d) Perimeter and Area: Using ratio of length to width
3. Given Perimeter or Area and ratio of length to width find the length or width.
e) Proportions
4. Solve for x.
7
15

x x 8
5. You paid $18 at a gas station for 12 gallons of gasoline. How much would 48
gallons of gasoline cost?
A
f) Geometric Mean - (know how to _______________________________ ______________________ )
6. Find the geometric Mean of 8 and 16.
e) Scale and scale drawing
7. A toy model of an aircraft has a scale of 3 in :4 ft. The aircraft has a
wingspan of 64 ft. Find the model’s wingspan in inches
Similar Polygons must have the following characteristics:
__________________________________ angles are ____________________
Corresponding _______________ _______________________ are __________________________
a) Similarity
Statement
b) Ratio of Sides
c) Ratio of Perimeters
8. Two triangles are similar. The sides of the first triangle are 7, 9, and 11,
the smallest side of the second triangle is 21. Find the perimeter of the
second triangle.
9. Two polygons are similar. If the ratio of the perimeters is 7:4, find the ratio
corresponding sides.
d) Ratio of Areas
10. The areas to two similar polygons are in the ration 25:81. Find the ration
of the corresponding sides.
Similar Triangles and Proving Similar Triangles
11.
What similarity theorem
proves that the two triangles
are similar?
12. Two ladders are leaned against the wall such that they make the same angle
with the ground. The 10’ ladder reaches 8’ up the wall. How much further up the
wall does the 18’ ladder reach?
13. Alma is 5 feet tall and casts a 7 foot shadow. At the same time, a tree casts a 21
foot shadow. The triangles formed are similar. Find the height of the tree (in feet).
Proving Triangles are Similar: use _______, __________, and ___________ Theorems
REVIEW QUIZ!! FOR EXAMPLES
14.
Using Proportionality Theorems
Triangle Proportionality
15.
3 Parallel Lines Proportionality
17.
16.
Triangle Angle Bisector
Proportionality