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Do Now Find the supplement of each angle. 1.83° 2.35° 3.165° 4.73° 5.124° Copyright © 2005 Pearson Education, Inc. Slide 1-1 Section 1.2 Angle Relationships and Similar Triangles Objective: SWBAT use geometric properties to identify similar triangles and angle relationships. Copyright © 2005 Pearson Education, Inc. Vertical Angles Vertical Angles have equal measures. Q R M N P The pair of angles NMP and RMQ are vertical angles. Do you see another pair of vertical angles? Copyright © 2005 Pearson Education, Inc. Slide 1-3 Parallel Lines Parallel lines are lines that lie in the same plane and do not intersect. When a line q intersects two parallel lines, q, is called a transversal. Eight angles are now formed. Transversal q m parallel lines n Copyright © 2005 Pearson Education, Inc. Slide 1-4 Angles and Relationships q m n Name Angles Rule Alternate interior angles 4 and 5 3 and 6 Angles measures are equal. Alternate exterior angles 1 and 8 2 and 7 Angle measures are equal. Interior angles on the same side of the transversal 4 and 6 3 and 5 Angle measures add to 180. Corresponding angles 2 & 6, 1 & 5, 3 & 7, 4 & 8 Angle measures are equal. Copyright © 2005 Pearson Education, Inc. Slide 1-5 Finding Angle Measures Find the measure of each marked angle, given that lines m and n are parallel. (6x + 4) (10x 80) m n The marked angles are alternate exterior angles, which are equal. Copyright © 2005 Pearson Education, Inc. 6 x 4 10 x 80 84 4 x 21 x One angle has measure 6x + 4 = 6(21) + 4 = 130 and the other has measure 10x 80 = 10(21) 80 = 130 Slide 1-6 Finding Angle Measures B m<A = 58° C D Z W Y X Copyright © 2005 Pearson Education, Inc. Slide 1-7 Angle Sum of a Triangle Take your given triangle. Tear each corner from the triangle. (so you now have 3 pieces) Rearrange the pieces so that the 3 pieces form a straight angle. Convincing?!? The sum of the measures of the angles of any triangle is 180. Copyright © 2005 Pearson Education, Inc. Slide 1-8 Applying the Angle Sum The measures of two of the angles of a triangle are 52 and 65. Find the measure of the third angle, x. Solution 52 65 x 180 117 x 180 x 63 65 x 52 Copyright © 2005 Pearson Education, Inc. Slide 1-9 Applying the Angle Sum The measures of two of the angles of a triangle are 48 and 61. Find the measure of the third angle, x. Solution: 48 x 61 Copyright © 2005 Pearson Education, Inc. Slide 1-10 Types of Triangles: Angles Copyright © 2005 Pearson Education, Inc. Slide 1-11 Types of Triangles: Sides Copyright © 2005 Pearson Education, Inc. Slide 1-12 Homework Page 14-16 # 4, 6, 12, 13, 16, 18, 26, 30, 34 Copyright © 2005 Pearson Education, Inc. Slide 1-13 Do Now Find the measures of all the angles. (2x – 21)° Copyright © 2005 Pearson Education, Inc. (5x – 129)° Slide 1-14 Section 1.2…Day 2 Angle Relationships and Similar Triangles Objective: SWBAT use geometric properties to identify similar triangles and angle relationships. Copyright © 2005 Pearson Education, Inc. Conditions for Similar Triangles Similar Triangles are triangles of exactly the same shape but not necessarily the same size. Corresponding angles must have the same measure. Corresponding sides must be proportional. (That is, their ratios must be equal.) Copyright © 2005 Pearson Education, Inc. Slide 1-16 Finding Angle Measures Triangles ABC and DEF are similar. Find the measures of angles D and E. D Since the triangles are similar, corresponding angles have the same measure. Angle D corresponds to angle A which = 35 A 112 35 F C 112 33 Copyright © 2005 Pearson Education, Inc. E Angle E corresponds to angle B which = 33 B Slide 1-17 Finding Side Lengths Triangles ABC and DEF are similar. Find the lengths of the unknown sides in triangle DEF. 32 64 16 x 32 x 1024 x 32 D A 16 112 35 64 F 32 C 112 33 48 Copyright © 2005 Pearson Education, Inc. To find side DE. B E To find side FE. 32 48 16 x 32 x 768 x 24 Slide 1-18 Application A lighthouse casts a shadow 64 m long. At the same time, the shadow cast by a mailbox 3 feet high is 4 m long. Find the height of the lighthouse. The two triangles are similar, so corresponding sides are in proportion. 3 x 4 64 4 x 192 x 48 3 4 x The lighthouse is 48 m high. 64 Copyright © 2005 Pearson Education, Inc. Slide 1-19 Homework Page 17-18 # 42-56 (evens) Copyright © 2005 Pearson Education, Inc. Slide 1-20

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