Download Mod 1 - Aim #3 - Manhasset Schools

Aim #3: How do we solve for unknown angles in a triangle?
CC Geometry H
Do Now: Find the measure of angle x:
Explain your calculations.
Figure: A (two-dimensional) figure is a set of points in a plane.
examples: triangle, square, rectangle, etc.
Angles of a Triangle : Every ΔABC determines three angles, ≮BAC, ≮ABC, and
≮ACB.
Interior of a Triangle : A point lies in the interior of a triangle if it lies in the
interior of each of the angles of the triangle.
Exterior Angle of a Triangle : Let ≮ABC be an interior angle of a ΔABC, and let D
be a point on AB such that B is between A and D. Then ≮CBD is an exterior angle
of ΔABC. Label the diagram:
Triangle Angle Sum Theorem
The sum of the 3 angle measures of any triangle is _______ degrees.
TYPES OF TRIANGLES
Type of
Triangle
Isosceles
Properties
• at least 2 sides are =
• at least 2 angles are =
• If two sides are = , then the opposite ≮s are =.
• If two ≮s are = , then the opposite sides are =.
• Base angles of an isosceles triangle are =.
Scalene
• No sides are =
• No angles are =
• An equilateral Δ has all sides =.
Equilateral
Equiangular
• An equiangular Δ has all angles =.
• A regular triangle has =≮s and = sides.
• If all sides of a Δ are =, all ≮s are =.
• If all ≮s of a Δ are =, all sides are =.
• Each angle measures _____.
Diagram
Solve for x:
a)
b) ∆ Exterior Angle Theorem
In any triangle, the measure of the exterior angle is equal to the sum of the
measures
of the ___________________ _________________ angles, also known as
________________ ___________________ angles.
Practice:
In each figure, determine the measures of the unknown (labeled) angles. Give
reasons for your calculations.
2.
1.
m≮a = _______
3.
m≮c = _______
m≮d = _______
m≮b = _____
4.
m≮f = _______
5.
m≮g = _______
6.
m≮h = _______
7.
m≮i = _______
1250
1150
i
8. Draw a diagram for each problem. Find the answer.
a) Find the measure of the vertex angle of an isosceles triangle if an exterior
angle formed by extending the base measures 1120.
b) If the vertex angle of an isosceles triangle measures 400, find the measure of
either of the exterior angles formed by extending the base.
9.
m≮j = _______
10.
x = _______
d
0
(2x)0
(2x ­ 5)
d = _______
0
1130
Let's sum it up!!!
• The sum of the angle measures in a triangle is ____________°.
• An exterior angle of a triangle equals the sum of the two _________________
__________________ angles.
Common Core Geometry H
HW #3
Name ____________________________
Date _____________
1. Find the measures of angles a and b. Explain your calculations.
In problems 2-6, determine the measures of the unknown (labeled) angles. Give
reasons for your calculations.
2.
m≮k = _____
m≮e = _____
3.
4.
5.
950
390
a
580
b
m≮a = _____
m≮b = _____
(2x + 9)0
6.
(3x ­ 1)0
m≮c = _____
c
(x + 12)0
420
7. Find the value of x:
a.
3x ­ 10
b.
x
80o
x
25
o
c.
x + 15
d. Segment P is || to segment L
P
120o
8x ­ 2
15x
L
140o
x