Do Now Find the supplement of each angle

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Do Now Find the supplement of each angle. 1. 83° 2. 35° 3. 165°

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

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 have equal measures. Q R M N P The pair of 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

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

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

Finding Angle Measures Find the measure of each marked angle, given that lines m and n are parallel. (6 x + 4) (10 x 80) m n The marked angles are alternate exterior angles, which are equal. Copyright © 2005 Pearson Education, Inc. One angle has measure 6 x + 4 = 6(21) + 4 = 130 and the other has measure 10 x 80 = 10(21) 80 = 130 Slide 1 -6

Finding Angle Measures B m<A = 58° C D Z W Y X Copyright

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

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

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 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

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: Angles Copyright © 2005 Pearson Education, Inc. Slide 1 -11

Types of Triangles: Sides Copyright © 2005 Pearson Education, Inc. Slide 1 -12

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

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. (2 x – 21)° Copyright

Do Now Find the measures of all the angles. (2 x – 21)° Copyright © 2005 Pearson Education, Inc. (5 x – 129)° Slide 1 -14

Section 1. 2…Day 2 Angle Relationships and Similar Triangles Objective: SWBAT use geometric properties

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 are triangles of exactly the same shape but not necessarily

Conditions for 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

Finding Angle Measures Triangles ABC and DEF are similar. Find the measures of angles D and E. n n D A 112 35 C F 112 33 Copyright © 2005 Pearson Education, Inc. E n Since the triangles are similar, corresponding angles have the same measure. Angle D corresponds to angle A which = 35 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

Finding Side Lengths Triangles ABC and DEF are similar. Find the lengths of the unknown sides in triangle DEF. n To find side DE. n To find side FE. D A 16 112 35 64 F E 32 C 112 33 B 48 Copyright © 2005 Pearson Education, Inc. Slide 1 -18

Application n A lighthouse casts a shadow 64 m long. At the same time,

Application n 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. n The two triangles are similar, so corresponding sides are in proportion. n The lighthouse is 48 m high. 3 4 x 64 Copyright © 2005 Pearson Education, Inc. Slide 1 -19

Homework Page 17 -18 # 42 -56 (evens) Copyright © 2005 Pearson Education, Inc.

Homework Page 17 -18 # 42 -56 (evens) Copyright © 2005 Pearson Education, Inc. Slide 1 -20

Severe Angle Blocking Severe Angle Blocking Severe AngleSevere Angle Blocking Severe Angle Blocking Severe Angle
Angle and Angle Measure Angles and Angle MeasureAngle and Angle Measure Angles and Angle Measure
ANGLE MODULATION Angle Modulation Introduction Types of AngleANGLE MODULATION Angle Modulation Introduction Types of Angle
Reference Angle Reference angle the positive acute angleReference Angle Reference angle the positive acute angle
Angle Bingo Find the size of angle markedAngle Bingo Find the size of angle marked
Find the measure of each numbered angle andFind the measure of each numbered angle and
Reference Angles Find the reference angle and FindReference Angles Find the reference angle and Find
EXAMPLE 3 Find an angle measure Find mEXAMPLE 3 Find an angle measure Find m
1 Find the missing angle 7 Find the1 Find the missing angle 7 Find the
Do Now Classify each angle as acute rightDo Now Classify each angle as acute right
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