Do Now Find the supplement of each angle. 83° 35° 165° 73° 124°

Section 1.2 Angle Relationships and Similar Triangles Objective: SWBAT use geometric properties to identify similar triangles and angle relationships.

Vertical Angles Vertical Angles have equal measures. The pair of angles NMP and RMQ are vertical angles. Do you see another pair of vertical angles? M Q R P N

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. m n parallel lines q Transversal

Angles and Relationships m n q Angle measures are equal. 2 & 6, 1 & 5, 3 & 7, 4 & 8 Corresponding angles Angle measures add to 180. 4 and 6 3 and 5 Interior angles on the same side of the transversal 1 and 8 2 and 7 Alternate exterior angles Angles measures are equal. 4 and 5 3 and 6 Alternate interior angles Rule Angles Name

Finding Angle Measures Find the measure of each marked angle, given that lines m and n are parallel. The marked angles are alternate exterior angles, which are equal. One angle has measure 6x + 4 = 6(21) + 4 = 130 and the other has measure 10x  80 = 10(21)  80 = 130 m n (10x  80) (6x + 4)

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

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.

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

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: 61 48 x

Types of Triangles: Angles

Types of Triangles: Sides

Homework Page 14-16 # 4, 6, 12, 13, 16, 18, 26, 30, 34

Find the measures of all the angles. Do Now Find the measures of all the angles. (2x – 21)° (5x – 129)°

Section 1.2…Day 2 Angle Relationships and Similar Triangles Objective: SWBAT use geometric properties to identify similar triangles and angle relationships.

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.)

Finding Angle Measures Triangles ABC and DEF are similar. Find the measures of angles D and E. 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 A C B F E D 35 112 33

Finding Side Lengths Triangles ABC and DEF are similar. Find the lengths of the unknown sides in triangle DEF. To find side DE. To find side FE. A C B F E D 35 112 33 32 48 64 16

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. The lighthouse is 48 m high. 64 4 3 x

Homework Page 17-18 # 42-56 (evens)