Analytical Geometry
Name__________________________
Study Guide Unit 1 Similarity
1. Draw the image of the figure after a dilation with a scale factor of ½
and the center of dilation at (3, 0)
2. Use the definition of similarity in terms of similarity transformation to
determine whether the two figures are similar. Explain your answer.
3. Fill in the blank.
Two triangles are similar if ___________________, and ________________.
4. If
name the congruent angles. ___________,
______________, _________________.
5. If
name the proportional sides
_________________________
6. What kind of triangles will always be similar?____________________
Explain why they must be
similar._________________________________
7. Identify which triangles are similar. Explain why they are similar.
8. Explain why the two figures are similar, then find the value of x.
9.
. What is the scale factor?________
10.Using the figure above and the similarity statement, find the lengths of
the missing sides __________, _______________
11. Determine the perimeter of both triangles____________, __________
12.Determine the area of both triangles.____________, _______________
A poster of the tallest building in the world hangs in a hallway. The
scale of the poster is 0.5 inches = 45 feet.
13. The height of the tallest building in the world, Burj Khalifa,is about
30.25 inches on the poster. What is the actual height of Burj Khalifa?
14. The height of the tallest building in the United States, Willis Tower
(formerly known as Sears Tower), is about 16 inches on the poster.
What is the actual height of Willis Tower?
15.How much taller is Burj Khalifa than Willis Tower?
Complete the following for each proof.
16. Prove that if a line parallel to one side of a triangle divides the other
two sides proportionally.
17. The Pythagorean Theorem using similarity.
18. Vertical angles are congruent.
Step 1: m∠1 + m∠3 = _________because of the Linear Pair postulate
m∠2 + m∠3 = _____________because of the Linear Pair postulate
Step 2: Set the two equations equal to each
m∠2 + m∠3 = _____________________
Step 3: Subtract m∠3 from both sides
19.When a transversal crosses parallel lines, alternate interior angles are
congruent.
If angle 1 is congruent to angle 5,