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7.4 Similar Polygons w/equations (Due 4/12/22)

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Last updated about 1 year ago
29 questions
Note from the author:
Essential Question: If you know two figures are similar, what can you determine about
measures of corresponding angles and lengths Learning Target: Students will be able to construct proportions from similar polygons and use them to determine the measures of the corresponding angles and side lengths of those polygons. Complete the entire document and show all work for credit.
Essential Question: If you know two figures are similar, what can you determine about
measures of corresponding angles and lengths Learning Target: Students will be able to construct proportions from similar polygons and use them to determine the measures of the corresponding angles and side lengths of those polygons. Complete the entire document and show all work for credit.
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Day 1 (4/11/22)

Concept Review

Question 1
1.

What is the name of the relationship between angle 5 and angle 7?

Question 2
2.

What is the relationship between angle 2 and angle 6?

Question 3
3.

Select all the vertical angles to ∠6

Question 4
4.

What is the value of x?



Question 5
5.

What is the value of z?


Similar Polygons

Question 6
6.

What is the correct order of steps to solve this similarity problem?

If △DEF ~ △HJG; find x


  1. x=20
  2. Rewrite the similarity statement so that you can line up the corresponding letters from each polygon:
  3. Simplify the equation to
  4. Divide both sides of the equation by 9:
  5. Replace the all the sides with numbers:
  6. Cross multiply to make the equation:
  7. JG is the side that has to be in the proportion created because it contains x, so create a proportion using corresponding sides from each triangle:
Question 7
7.

USE THE SIMILARITY RELATIONSHIP TO FIND THE INDICATED VALUE:

If △DEF ~ △HJG; find x


Question 8
8.

What is the correct order of steps to solve this similarity problem?

If △QRS ~ △TUV; find x


  1. Rewrite the similarity statement so that you can line up the corresponding letters from each polygon:
  2. Simplify the equation to
  3. Cross multiply to make the equation:
  4. Subtract 270 from both sides of the equation:

  5. Replace the all the sides with numbers:
  6. UT is the side that has to be in the proportion created because it contains x, so create a proportion with UT using corresponding sides from each triangle:
  7. Divide both side of the equation by 54:
  8. x=11
Question 9
9.

USE THE SIMILARITY RELATIONSHIP TO FIND THE INDICATED VALUE:

If △QRS ~ △TUV; find x

Question 10
10.

USE THE SIMILARITY RELATIONSHIP TO FIND THE INDICATED VALUE:

If △AGM ~ △KXD; find x

Question 11
11.

USE THE SIMILARITY RELATIONSHIP TO FIND THE INDICATED VALUE:

If △TLY ~ △CHK; find x

Question 12
12.

USE THE SIMILARITY RELATIONSHIP TO FIND THE INDICATED VALUE:

If △BCD ~ △FGE; find FE

Question 13
13.

USE THE SIMILARITY RELATIONSHIP TO FIND THE INDICATED VALUE:

If △MNP ~ △QRP; find x

Question 14
14.

USE THE SIMILARITY RELATIONSHIP TO FIND THE INDICATED VALUE:

If ▱KLMN ~ ▱PQRS; find x

Day 2 (4/12/22)

Concept Review

Question 15
15.

Determine the scale factor of the dilation that transformed triangle ABC to triangle A'B'C'.

Question 16
16.

What is the dilation of △ ABC → △ A'B'C'? Page 12
A (0, 4) B (5,5) C (3,3)
A’ (0, 8) B’ (10, 10) C’ (6, 6)

Part II

Triangle Inequalities



Question 17
17.
Determine if the side lengths could form a triangle. Use an inequality to prove your answer.
18 in, 6 in, 13 in
_______+_______ =_______; and 19 _______ 18

Therefore this _______ a triangle
Part I

Isosceles and Equilateral Triangles
Question 18
18.
Find the measure of the indicated angle.

m∠C=_______
m∠A=_______
Question 19
19.
Solve for x.

Find the length of the indicated side.

x=_______
DE=_______
m∠E=_______
Question 20
20.
Solve for x.

Find the length of the indicated side.

x=_______
OM=_______
m∠G=_______

Triangle Proportionality

Question 21
21.

What is the value of x?

Question 22
22.

What is the value of x?

Question 23
23.

What is the value of x?

Question 24
24.

What is the value of x?

Day 3 (4/13/22)

Special Triangle Similarity Theorems


Question 25
25.

Use the new "side-splitter" Theorem to create a proportion to solve for x.

Question 26
26.

Use the new "side-splitter" Theorem to solve for x.

Question 27
27.

Use the new "side-splitter" Theorem to create a proportion to solve for x.

Question 28
28.

Use the new "side-splitter" Theorem to solve for x.

Question 29
29.

Use the new "side-splitter" Theorem to solve for x.