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Chapter 7.2 and 7.3. Similar Polygons and Triangles. Concept. Use a Similarity Statement. If Δ ABC ~ Δ RST , list all pairs of congruent angles and write a proportion that relates the corresponding sides. A.  HGK   QPR B. C.  K   R D.  GHK   QPR.

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chapter 7 2 and 7 3

Chapter 7.2 and 7.3

Similar Polygons and Triangles

slide3

Use a Similarity Statement

If ΔABC ~ ΔRST, list all pairs of congruent angles and write a proportion that relates the corresponding sides.

slide4

A.HGK  QPR

B.

C.K  R

D.GHK  QPR

If ΔGHK ~ ΔPQR, determine which of the following similarity statements is not true.

slide5

Identify Similar Polygons

A. MENUSJoe is designing a new menu for the restaurant where he works. Determine whether the size for the new menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning.

Original Menu: New Menu:

slide6

Identify Similar Polygons

B. MENUSJoe is designing a new menu for the restaurant where he works. Determine whether the size for the new menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning.

Original Menu: New Menu:

slide7

A.BCDE ~ FGHI, scale factor =

B. BCDE ~ FGHI, scale factor =

C. BCDE ~ FGHI, scale factor =

D. BCDE is not similar to FGHI.

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Original: New:

A.Zemira is a wedding planner who is making invitations. Determine whether the size for the new invitations is similar to the original invitations used. If so, choose the correct similarity statement and scale factor.

slide8

A. BCDE ~ WXYZ, scale factor =

B. BCDE ~ WXYZ, scale factor =

C. BCDE ~ WXYZ, scale factor =

D. BCDE is not similar to WXYZ.

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Original: New:

B. Zemira is a wedding planner who is making invitations. Determine whether the size for the new invitations is similar to the original invitations used. If so, choose the correct similarity statement and scale factor.

slide9

Use Similar Figures to Find Missing Measures

  • The two polygons are
  • similar. Find x.
slide10

Use Similar Figures to Find Missing Measures

B.The two polygons are similar. Find y.

slide11

A. The two polygons are similar. Solve for a.

A.a = 1.4

B.a = 3.75

C.a = 2.4

D.a = 2

slide14

Use a Scale Factor to Find Perimeter

If ABCDE ~ RSTUV, find the scale factor of ABCDE to RSTUV and the perimeter of each polygon.

slide15

If LMNOP ~ VWXYZ, find the perimeter of each polygon.

A. LMNOP = 40, VWXYZ = 30

B. LMNOP = 32, VWXYZ = 24

C. LMNOP = 45, VWXYZ = 40

D. LMNOP = 60, VWXYZ = 45

slide17

Use the AA Similarity Postulate

A.Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.

slide18

Use the AA Similarity Postulate

B.Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.

slide19

A.Determine whether the triangles are similar. If so, write a similarity statement.

A.Yes; ΔABC ~ ΔFGH

B. Yes; ΔABC ~ ΔGFH

C. Yes; ΔABC ~ ΔHFG

D. No; the triangles are not similar.

slide20

B.Determine whether the triangles are similar. If so, write a similarity statement.

A. Yes; ΔWVZ ~ ΔYVX

B. Yes; ΔWVZ ~ ΔXVY

C. Yes; ΔWVZ ~ ΔXYV

D. No; the triangles are not similar.

slide22

Use the SSS and SAS Similarity Theorems

  • Determine whether
  • the triangles are similar.
  • If so, write a similarity statement. Explain your reasoning.

Answer:So, ΔABC ~ ΔDEC by the SSS Similarity Theorem.

slide23

Use the SSS and SAS Similarity Theorems

B.Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.

Answer:Since the lengths of the sides that include M are proportional, ΔMNP ~ ΔMRS by the SAS Similarity Theorem.

slide24

A.Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data.

A. ΔPQR ~ ΔSTR by SSS Similarity Theorem

B. ΔPQR ~ ΔSTR by SAS Similarity Theorem

C. ΔPQR ~ ΔSTR by AA Similarity Theorem

D. The triangles are not similar.

slide25

B.Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data.

A. ΔAFE ~ ΔABC by SAS Similarity Theorem

B. ΔAFE ~ ΔABC by SSS Similarity Theorem

C. ΔAFE ~ ΔACB by SAS Similarity Theorem

D. ΔAFE ~ ΔACB by SSS Similarity Theorem

slide26

ALGEBRAGiven , RS = 4, RQ = x + 3, QT= 2x + 10, UT = 10, find RQ and QT.

Parts of Similar Triangles

slide27

ALGEBRAGiven AB = 38.5, DE = 11, AC = 3x + 8, and CE =x + 2, find AC.

A. 2

B. 4

C. 12

D. 14

slide28

Indirect Measurement

SKYSCRAPERSJoeury wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 p.m. The length of the shadow was 2 feet. Then he measured the length of Sears Tower’s shadow and it was 242 feet at the same time. What is the height of the Sears Tower?

Understand Make a sketch of the situation.

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LIGHTHOUSESOn her tripalong the East coast, Jennie stops to look at the tallest lighthouse in the U.S. located at Cape Hatteras, North Carolina.At that particular time of day, Jennie measures her shadow to be 1 foot 6 inches in length and the length of the shadow of the lighthouse to be 53 feet6 inches. Jennie knows that her heightis 5 feet 6 inches. What is the height ofthe Cape Hatteras lighthouse to the nearest foot?

A. 196 ft B. 39 ft

C. 441 ft D. 89 ft

slide31

If ΔRST and ΔXYZ are two triangles such that = , which of the following would be sufficient to prove that the triangles are similar? A BC R  S D

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Sufficient Conditions

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