Lesson 9.1 Skills Practice

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Lesson 9.1 Skills Practice!"#$ %"&$ Epanding Your Mind Dilations of Triangles Vocabular Choose the term or terms from the bo to best complete each sentence. dilation center of dilation scale factor enlargement reduction dilation factor 1. The, or, is the ratio formed when comparing the distance of the image from the center of dilation to the distance of the original figure from the center of dilation.. In mathematics, are transformations that produce images that are the same shape as the original image, but not the same size. 3. When the scale factor is less than one, the image is called a(n).. When the scale factor of a dilation is greater than one, the image is called a(n). 5. In a dilation, each point on the original figure is moved along a straight line and the straight line is drawn from a fied point known as the. Problem Set Dilate each triangle with P as the center of dilation and the given scale factor. 1. Dilate triangle ABC with P as the center of dilation and a scale factor of. B B P C A C A Chapter 9 Skills Practice 1

Lesson 9.1 Skills Practice page. Dilate triangle ABC with P as the center of dilation and a scale factor of 3. P B A C 3. Dilate triangle ABC with P as the center of dilation and a scale factor of 1. P B A C. Dilate triangle ABC with P as the center of dilation and a scale factor of 1 3. P B A C Chapter 9 Skills Practice

Lesson 9.1 Skills Practice page 3!"#$ %"&$ 5. Dilate triangle ABC with P as the center of dilation and a scale factor of. P B A C. Dilate triangle ABC with P as the center of dilation and a scale factor of 1. P B A C Chapter 9 Skills Practice 3

Lesson 9.1 Skills Practice page Dilate each triangle with P as the center of dilation and the given scale factor. 7. Dilate triangle ABC on the coordinate plane using the origin (, ) as the center of dilation and a scale factor of. 1 1 B (,) B(3,5) A (,) C (,) A(,) C(5,) 1 1. Dilate triangle ABC on the coordinate plane using point A (3, 3) as the center of dilation and a scale factor of. 1 1 C(3,7) A(3,3) B(9,3) 1 1 Chapter 9 Skills Practice

Lesson 9.1 Skills Practice page 5!"#$ %"&$ 9. Dilate triangle ABC on the coordinate plane using the origin (, ) as the center of dilation and a scale factor of 1. 1 1 B(,1) A(,) C(1,) 1 1. Dilate triangle ABC on the coordinate plane using the origin (, ) as the center of dilation and a scale factor of 1. B(,) 1 1 A(,) C(,) 1 1 Chapter 9 Skills Practice 5

Lesson 9.1 Skills Practice page 11. Dilate triangle ABC on the coordinate plane using point A (, 1) as the center of dilation and a scale factor of 3. 1 1 B(,) A(,1) C(,1) 1 1 1. Dilate triangle ABC on the coordinate plane using point A (3, 3) as the center of dilation and a scale factor of 1 3. 1 B(3,) 1 A(3,3) C(15,3) 1 1 Chapter 9 Skills Practice

Lesson 9. Skills Practice!"#$ %"&$ Look-Alikes Similar Triangles Vocabular Define the term in our own words. 1. similar triangles Problem Set Identif the congruent corresponding angles and write ratios to identif the proportional sides of the similar triangles in each problem. 1. nabc, na9b9c9 B P B A C A C Congruent corresponding angles: /A > /A9 /B > /B9 /C > /C9 Proportional Sides: AB A9B9 5 BC B9C9 5 CA C9A9 Chapter 9 Skills Practice 7

Lesson 9. Skills Practice page. ndef, nd9e9f9 P E E D F D F 3. nabc, ndef P B E A C D F Chapter 9 Skills Practice

Lesson 9. Skills Practice page 3!"#$ %"&$. nfgh, nxyz P G F H Y X Z 5. nabc, nmnp Chapter 9 Skills Practice 9

Lesson 9. Skills Practice page. nrst, nxyz 7. nxyz, nghj. nklm, nrst 9 Chapter 9 Skills Practice

Lesson 9. Skills Practice page 5!"#$ %"&$ Determine each missing measure. 9. Given: nace, nbcd C BD AE 5 CD CE cm 5 cm cm 5 cm B 5 cm D? 5 5 () 5 5 A cm E 5 CE 5 cm CD 1 DE 5 CE cm 1 DE 5 cm DE 5 cm Chapter 9 Skills Practice 91

Lesson 9. Skills Practice page. Given: nnmr, nnpq P? M 3 N R Q 11. Given: nrtu, nrsv T? S R V U 9 Chapter 9 Skills Practice

Lesson 9. Skills Practice page 7!"#$ %"&$ 1. Given: nnyz, nmyx Y cm cm M 3 cm X N? Z Chapter 9 Skills Practice 93

Lesson 9. Skills Practice page 13. Given: nabc, nxyz B Z? X cm Y cm A 3 cm C 1. Given: nnmp, nxyz M Z cm X Y cm 1 cm N? P 9 Chapter 9 Skills Practice

Lesson 9.3 Skills Practice!"#$ %"&$ Prove It! AA, SAS, and SSS Similarit Theorems Vocabular Define each theorem in our own words. 1. SAS Similarit Theorem. AA Similarit Theorem 3. SSS Similarit Theorem Chapter 9 Skills Practice 95

Lesson 9.3 Skills Practice page Problem Set Determine if the triangles in each problem are similar. 1. Use the AA Similarit Theorem and a protractor to determine if nabc and na9b9c9 are similar triangles. The measures of /A and /A9 are equal. A Angle B and /B9 are both right angles. 1 The measures of /B and /B9 are equal. 1 The two triangles are similar b the AA Similarit Theorem. B A C B C 1 1. Use the AA Similarit Theorem and a protractor to determine if nabc and na9b9c9 are similar triangles. 1 1 B A B C A C 1 1 9 Chapter 9 Skills Practice

Lesson 9.3 Skills Practice page 3!"#$ %"&$ 3. Use the SAS Similarit Theorem and a protractor to determine if nabc and na9b9c9 are similar triangles. B (13,15) 1 1 B (,11) A (,7) C (,7) A (13,13) C (17,13) 1 1 Chapter 9 Skills Practice 97

Lesson 9.3 Skills Practice page. Use the SAS Similarit Theorem and a protractor to determine if nabc and na9b9c9 are similar triangles. 1 1 B (5,) A (,) C (,) B (13,7) C (1.5,) A (11.5,) 1 1 9 Chapter 9 Skills Practice

Lesson 9.3 Skills Practice page 5!"#$ %"&$ 5. Use the SSS Similarit Theorem to determine if nabc and na9b9c9 are similar triangles. 1 1 C (7,11) C (15,9) B (,7) A (1,7) A (3,3) B (11,3) 1 1 Chapter 9 Skills Practice 99

Lesson 9.3 Skills Practice page. Use the SSS Similarit Theorem to determine if nabc and na9b9c9 are similar triangles. 1 1 B (,11) A (11,13) C (15,13) B (11,) A (,) C (1,) 1 1 7 Chapter 9 Skills Practice

Lesson 9.3 Skills Practice page 7!"#$ %"&$ Determine if the triangles in each are similar b AA, SAS, or SSS. 7. 95 95 The triangles are similar b AA.. 3 3 7 cm 7 cm 1 cm 1 cm 9. cm 7 cm 3.5 cm 3 cm Chapter 9 Skills Practice 71

Lesson 9.3 Skills Practice page. cm cm cm 5 cm cm cm 11. cm 5.5 cm cm 1 cm 11 cm cm 1. 7 Chapter 9 Skills Practice

Lesson 9. Skills Practice!"#$ %"&$ Back on the Grid Similar Triangles on the Coordinate Plane Problem Set Verif that the triangles in each are similar. 1. Triangle DEF is the image that resulted from a dilation of nabc. Use the SAS Similarit Theorem to determine whether nabc is similar to ndef. 1 Corresponding Sides AB and DE : AB 5 DE 5 1 E (,) DE AB 5 5 B (,5) D (,) F (1,) Corresponding Sides AC and DF : A (,3) C (,3) AC 5 1 1 DF 5 DF AC 5 5 DE AB 5 DF AC 5 Corresponding Angles /A and /D: Angle A and /D are both right angles. The measures of /A and /D are equal. The two triangles are similar b the SAS Similarit Theorem. Chapter 9 Skills Practice 73

Lesson 9. Skills Practice page. Triangle DEF is the image that resulted from a dilation of nabc. Use the SAS Similarit Theorem and a protractor to determine whether nabc is similar to ndef. 1 1 B (1,) E (,9) A (,) C (,) D (,5) F (,5) 1 1 7 Chapter 9 Skills Practice

Lesson 9. Skills Practice page 3!"#$ %"&$ 3. Triangle DEF is the image that resulted from a dilation of nabc. Use the SSS Similarit Theorem to determine whether nabc is similar to ndef. 1 1 B (,) A (,) C (,) E (17,) D (5,) F (17,) 1 1 Chapter 9 Skills Practice 75

Lesson 9. Skills Practice page. Triangle DEF is the image that resulted from a dilation of nabc. Use the SSS Similarit Theorem to determine whether nabc is similar to ndef. 1 1 A (1,11) B (11,11) D (13,11) E (,11) C (,1) F (15.5,) 1 1 7 Chapter 9 Skills Practice

Lesson 9. Skills Practice page 5!"#$ %"&$ 5. Dilate nabc to form ndef using point P (, ) as the center of dilation and a scale factor of. Use the AA Similarit Theorem and a protractor to determine whether nabc is similar to ndef. 1 1 B (,) A (,1) C (,1) P (,) 1 1 Chapter 9 Skills Practice 77

Lesson 9. Skills Practice page. Dilate nabc to form ndef using point P (, ) as the center of dilation and a scale factor of 1. Use the AA Similarit Theorem and a protractor to determine whether nabc is similar to ndef. 1 B (1,) 1 C (,1) A (9,) P (,) 1 1 7 Chapter 9 Skills Practice

Lesson 9. Skills Practice page 7!"#$ %"&$ 7. Dilate DABC to form ndef using point A (, 3) as the center of dilation and a scale factor of 3. Use the SAS Similarit Theorem to determine whether nabc is similar to ndef. 1 1 B (,) A (,3) C (7,3) 1 1 Chapter 9 Skills Practice 79

Lesson 9. Skills Practice page. Dilate nabc to form ndef using point A (, ) as the center of dilation and a scale factor of 1 3. Use the SAS Similarit Theorem to determine whether nabc is similar to ndef. 1 B (9,1) 1 A (,) C (,) 1 1 7 Chapter 9 Skills Practice

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