Unit 4 – Similar and Congruent Figures Study Guide Name Per.

1 Unit 4 Similar and Congruent Figures Study Guide Objective 1: Points, lines, segments, rays, and angles (Standards and ) Objective 2: Line notation and relationships (Standards and ) Objective 3: Congruent and Similar Figures (Standards and ) Objective 4: Congruent and Similar Figures (Standards and ) Objective 5: Corresponding parts of Similar Figures (Standards and ) Objective 6: Congruent triangles (Standards and ) Objective 7: Similar triangles (Standards and ) Objective 8: Similar triangles and proportions (Standards and ) Objective 9: WP: Similar triangles and proportions (Standards and ) Objective 10: Scale drawings (Standards and ) Test Day Objectives 1 5: _____ Test Day Objectives 1 10: _____ Objective 1: Points, lines, segments, rays, and angles (Standards and ) (Use your notes from class, the book, (pages 285 286), and the examples below.)

2 1. Use the correct notation to 2. Use the correct notation to 3. What word best describes the describe the figure below. illustrate an angle. figure An angle is represented by two Y Z rays meeting at their end points. A B C Since this is a line, the correct A line segment. notation is YZ . B A Objective 2: Line notation and relationships (Standards and ) (Use your notes from class, the book, (pages 285 286), and the examples below.) 1. Write the symbol 2. What is the best description 3. Which statement is true according to notation for the geometric of perpendicular lines? the diagram? figure. Then name what type of figure it is. A. Line segments that do not A B D s intersect C G B. Line segments that E A B intersect to form a right angle F u The notation is AB.

3 C. Lines that do not intersect q r t It is a ray. D. Lines that intersect to form a right angle A. q u q is not parallel to u. A. Perpendicular lines are B. r t r is not parallel to t. lines that intersect to form a C. t ^ q t is not perpendicular to q. right angle. D. u ^ t u is parallel to t. The correct answer is D. 1 Objectives 3 and 4: Congruent and Similar Figures (Standards and ) (See pages 288 290 in book for additional examples.) 1. Which best represents a pair of Similar Figures ? 2. Decide whether the two prisms are Similar . A. B. 28 7 9 36 13 52 C. D. Corresponding sides of Similar Figures are proportional. Are these? 28 36 52 =4 =4 =4. Since Similar Figures have the same shape, the 7 9 13 correct answer is C.

4 Yes, they are proportional, so the prisms are Similar . 3. Which figure appears to be Congruent ? 4. Fill in the blank to make the statement true. Similar polygons _____. A. Always have sides with equal measure. B. Never have sides with equal measure. C. sometimes have angles with equal measure. D. always have corresponding angles with equal measure. A. Only Similar Figures that are also Congruent have sides with equal measure. B. Similar Figures do have sides with equal measure Since Congruent Figures have the same shape and if they are also Congruent . C. Since enlarging or shrinking a figure has no the same size, the top left and the bottom right effect the size of the angles, they would always Figures are the ones that seem to be Congruent .

5 Have angles of equal measure. Therefore, D would be the correct answer. Objective 5: Corresponding parts of Similar Figures (Standards and ) (See pages 288 290 in book for additional examples.) 1. The Figures below are Similar . List the pairs of 2. The Figures below are Similar . List the pairs of corresponding sides. B C corresponding angles. Y V R S Q T A D X Z. We can tell by looking that ABCD ~TSRQ. U W Therefore, the following sides are corresponding: We can tell by looking that UVW ~ XYZ. QR and DC or RQ and CD Therefore, the following angles are corresponding: RS and CB or SR and BC U and X ST and BA or TS and AB V and Y W and Z QT and DA or TQ and AD 2 3. The Figures below are Similar . Which of the following is not a pair of corresponding sides?

6 B C R S A . QR and AB B . RS and BC C . ST and BA Q T D . QT and AD A D Since QRST ~ ABCD, all of the ones listed match up except ST and BA. ST matches up with CD and BA matches up with RQ . Objective 6: Congruent triangles (Standards and ) (See pages 288 290 in book for additional examples.) 1. Which figure appears to be Congruent ? 2. The two triangle shaped gardens are Congruent . Find the missing lengths and angle measures. e 29 o h ft 10 ft o o g f 61 90 ft d Since Congruent Figures have the same shape and the same size, the following would be true: d = ft e = 29 o Since Congruent Figures have the same shape and f = 90 o g = 61 o the same size, the top right and the bottom left Figures are the ones that seem to be Congruent .

7 H = ft 3. If ABC @ EDC, name each pair of Congruent angles and B D A C E A @ E AC @ EC B @ D AB @ ED ACB @ ECD BC @ DC. Remember, you cannot say C since Remember, when naming Congruent line there is more than one angle at that vertex. Segments, corresponding parts must be named in the same direction. 3 Objective 7: Similar triangles (Standards and ) (See pages 293 294 in book for additional examples.) 1. Given that DABC ~ DDEF , solve for x . A D Since the two triangles are Similar , we can set up a proportion to solve for x . Be sure to put the corresponding parts of the 19 10 x Figures in the corresponding positions in the proportion. 19 x E 7 F = Set up the proportion. 11 7 B 11 C 19 ( 7 ) = x Do the cross products and solve for x.

8 11 x = 12. 09 Check to see how the problem says to round or check the answers to see how they have rounded. 2. DBCD is Similar to DEFG . Find FG C C F F Since the two triangles are Similar , we can set up a proportion to find FG . Since FG on the smaller figure corresponds to the 55 50 11 50 on the larger figure and the 11 on the smaller figure x corresponds to 55 on the larger figure, be sure to put each pair in the corresponding positions. I have labeled FG as x . 55 11 B 35 D E G = Set up the proportion. 50 x 50( 11 ) x = Do the cross products and solve for x . 55 x = 10. 3. Triangle QRS is Similar to triangle TUV . Find the measure of x . R U Since the two triangles are Similar , the corresponding angles are equal.

9 53 o The angles of a triangle add up to 180 o . x T V To find x , add up the given angles and subtract from 180 o . o 63 Q S 63 + 53 = 116 x = 180 116 x = 64 o Don't forget to label!!! 4 4. Use Similar Figures to find x . This problem is made up of two triangles, the larger one and a smaller one inside the larger one. Think of them as two separate triangles. 9 ft To find x , write a proportion with the larger triangle's ratio on the x left and the smaller triangle's ratio on the right. 9 x 7 ft = Notice that the corresponding parts of the two triangles 17 . 5 7 ft are in corresponding positions in the proportion. 9( 7 ) x = Do the cross products and solve for x . 17 . 5 x = 3. 6 ft Don't forget to label!!! Objective 8: Similar triangles and proportions (Standards and ) (See pages 293 294 in book for additional examples.)

10 1. DABC and DXYZ are Similar . If AB , BC , and AC are 6 inches, 9 inches, and 14 inches respectively, and XY is 12 inches, find XZ to the nearest tenth. Draw and label two triangles according to the given information. B Y Since the two triangles are Similar , we can set up a proportion to solve for XZ . Pick a variable to represent side XZ . Be sure to put the corresponding parts of the Figures in the corresponding positions in the proportion. (Since 9 doesn't have a corresponding length on the other 6 in 9 in 12 in triangle, we will not be using it in our proportion.) 6 12 = Set up the proportion. 14 x A C X Z. 14 ( 12 ) 14 in x = x Do the cross products and solve for x . 6 x = 28 in If you get a decimal answer, check to see how the problem says to round or check the answers to see how they have rounded.