Download presentation

Presentation is loading. Please wait.

1
**4-2: Measuring Angles in Triangles**

Expectations: G1.2.1: Prove that the sum of the angle measures of a triangle is 180 and that the measure of an exterior angle of a triangle is the sum of the measures of the 2 remote interior angles. G1.2.2: Solve problems involving angle measure and side length of triangles. 3/25/2017 4-2: Measuring Angles in Triangles

2
**4-2: Measuring Angles in Triangles**

Linear Triples ∠A, ∠B and ∠C form a linear triple iff ∠A is adjacent to ∠B, ∠B is adjacent to ∠C, ∠A and ∠C have no points in common (other than the vertex) and the sum of their measures is 180. ∠A ∠B ∠C ∠A, ∠B and ∠C form a linear triple. 3/25/2017 4-2: Measuring Angles in Triangles

3
**Justify the sum of the measures of ∠A, ∠B and ∠C.**

3/25/2017 4-2: Measuring Angles in Triangles

4
**4-2: Measuring Angles in Triangles**

Triangle Sum Theorem: The sum of the measures of the angles of a triangle is _______°. 3/25/2017 4-2: Measuring Angles in Triangles

5
**Determine the value of x.**

C x A x - 8 B 58 3/25/2017 4-2: Measuring Angles in Triangles

6
**4-2: Measuring Angles in Triangles**

In triangle ABC below, the measure of ∠A is 20° and the measure of ∠B is 3 times larger than the measure of ∠C. What is the measure of angle B? 40° 60° 80° 120° 160° B C A 3/25/2017 4-2: Measuring Angles in Triangles

7
**Calculate the measures of each angle below.**

8x-12 7x+3 5x+9 A B 3/25/2017 4-2: Measuring Angles in Triangles

8
**4-2: Measuring Angles in Triangles**

If ∠A≅∠D and ∠C≅∠F, what may you conclude about ∠B and ∠E? Can you justify your conjecture? C F A B D E 3/25/2017 4-2: Measuring Angles in Triangles

9
**4-2: Measuring Angles in Triangles**

3/25/2017 4-2: Measuring Angles in Triangles

10
**4-2: Measuring Angles in Triangles**

Third Angle Congruence Theorem: If two angles of one triangle are _____________ to 2 angles of a second triangle, then the third angles are also _____________ . 3/25/2017 4-2: Measuring Angles in Triangles

11
**4-2: Measuring Angles in Triangles**

Exterior Angles An angle is an exterior angle of a triangle iff it is the union of one side of the triangle and the extension of the other side that shares the same vertex as the first side. 3/25/2017 4-2: Measuring Angles in Triangles

12
**4-2: Measuring Angles in Triangles**

Exterior Angles C ∠CBD is an exterior angle for ∆ABC A B D 3/25/2017 4-2: Measuring Angles in Triangles

13
**4-2: Measuring Angles in Triangles**

Exterior Angles C ∠ABE is an exterior angle for ∆ABC A B E 3/25/2017 4-2: Measuring Angles in Triangles

14
**4-2: Measuring Angles in Triangles**

Exterior Angles Because there are 2 exterior angles at each vertex, every triangle has a total of 6 exterior angles. 3/25/2017 4-2: Measuring Angles in Triangles

15
**4-2: Measuring Angles in Triangles**

Remote Interior Angles: A remote interior angle of a triangle is one of the 2 interior angles not adjacent to an exterior angle. Remote interior angles change depending on which interior angle is being discussed. 3/25/2017 4-2: Measuring Angles in Triangles

16
**4-2: Measuring Angles in Triangles**

Remote Interior Angles: ∠ __ and ∠__ are remote interior angles for exterior ∠BCD. B A C D 3/25/2017 4-2: Measuring Angles in Triangles

17
**4-2: Measuring Angles in Triangles**

Remote Interior Angles: ∠__ and ∠__ are remote interior angles for exterior ∠BAE. B E A C 3/25/2017 4-2: Measuring Angles in Triangles

18
**4-2: Measuring Angles in Triangles**

Exterior Angle Theorem: The measure of an exterior angle of a triangle is the sum of the measures of 3/25/2017 4-2: Measuring Angles in Triangles

19
**Exterior Angle Theorem: A Proof**

Given: ΔABC with exterior angle ∠BCD Prove: m∠BCD = m∠A + m∠B B A C D 3/25/2017 4-2: Measuring Angles in Triangles

20
**Given: ΔABC with exterior angle ∠BCD Prove: m∠BCD = m∠A + m∠B**

3/25/2017 4-2: Measuring Angles in Triangles

21
**4-2: Measuring Angles in Triangles**

What is the measure of ∠A? 124° A 52° First hour start here 4/19/05 3/25/2017 4-2: Measuring Angles in Triangles

22
**4-2: Measuring Angles in Triangles**

Corollary A corollary is a theorem that is easily proven by another theorem. 3/25/2017 4-2: Measuring Angles in Triangles

23
**Acute Angles Corollary**

The acute angles of a right triangle are ____________. A C B m∠A + m∠B = 3/25/2017 4-2: Measuring Angles in Triangles

24
**Obtuse Angle Corollary**

Right Angle Corollary There can be at most ___ right angle in a triangle. Obtuse Angle Corollary There can be at most ___ obtuse angle in a triangle. 3/25/2017 4-2: Measuring Angles in Triangles

25
**4-2: Measuring Angles in Triangles**

In triangle ABC, m∠A is 16 more than m∠B and m∠C is 29 more than m∠B. Determine the measure of each angle. 3/25/2017 4-2: Measuring Angles in Triangles

26
**4-2: Measuring Angles in Triangles**

3/25/2017 4-2: Measuring Angles in Triangles

27
**4-2: Measuring Angles in Triangles**

If AB is perpendicular to BC, determine the measures of all 8 numbered angles. 3/25/2017 4-2: Measuring Angles in Triangles

28
**4-2: Measuring Angles in Triangles**

Assignment: pages , # (odds), 36, 39, (all) 3/25/2017 4-2: Measuring Angles in Triangles

Similar presentations

OK

Warm-Up Exercises 1.90º 2. 72º Classify each angle as acute, obtuse, or right. 3.116º 4. How do you know that 1 = 2? ~ 2 1.

Warm-Up Exercises 1.90º 2. 72º Classify each angle as acute, obtuse, or right. 3.116º 4. How do you know that 1 = 2? ~ 2 1.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on work and energy for class 9th Means of communication for kids ppt on batteries Ppt on conference call etiquette you need to know Ppt on power system restructuring Creating ppt on ipad Ppt on power grid failure east Download ppt on coordinate geometry for class 9th science Ppt on ms word 2003 Mems display ppt online Ppt on food subsidy in india