Download The sum of the angles of a triangle is ______ degrees.

Aim 3 CC Geometry R
The sum of the angles of a triangle is ____________ degrees.
1
3
2
1
3
Name____________________
Common Core Geometry R
Date_____________
HW #2 (Missing angles and transversals)
Find the unknown (labeled) angles. Give reasons for your solutions.
1.
350
2.
1450
• If ll lines are cut by a transversal, alternate
interior angles are equal in measure. (350)
• Linear pairs form supplementary angles.
(answer)
810
• If ll lines are cut by a transversal, alternate
interior angles are equal in measure. (370)
• The sum of the angle measures in a triangle is
370
1800. (answer)
3. Draw an auxiliary line.
360
560
• If ll lines are cut by a transversal, alternate
interior angles are equal in measure.
• If ll lines are cut by a transversal, same side
interior angles are supplementary.
• Angle addition postulate (answer)
920
4. Draw an auxiliary line.
1170 630
1290 510
1140
• If ll lines are cut by a transversal,
corresponding angles are equal in measure.
(1170 and 1290)
• Linear pairs form supplementary angles.
(630 and 510)
5. Draw an auxiliary line.
• Angle addition postulate (1140)
460
460
500
• If ll lines are cut by a transversal, same side
interior angles are supplementary. (500)
• Angle addition postulate (460)
• If ll lines are cut by a transversal, alternate
interior angles are equal in measure.
OVER
6.
1440
b = _____
b
360
360
360
• Vertical angles are =. (360)
• If parallel lines are cut by a transversal,
corresponding angles are = in measure.
(360)
• If parallel lines are cut by a transversal,
same side interior angles are supplem.
(answer)
7.
a = _____
1400
1400
40
740
0
• If parallel lines are cut by a transversal,
same side interior angles are supplem.
• Angles that form a linear pair sum to
b = _____
1800.
740
• Vertical angles are =. (400)
a1400
660
400
b 740
• Adjacent angles on one side of a line sum to 1800.(740)
• If ll lines are cut by a transversal, alternate
interior angles are =. (answer)
8.
500
500
• If ll lines are cut by a transversal, alternate
interior angles are =. (500)
500
• If ll lines are cut by a transversal, alternate
interior angles are =. (500)
9.
980
f
820
• Vertical angles are = in meaure.(f)
• If parallel lines are cut by a transversal,
same side interior angles are supplem.
7x + 5 = 180
x = 25
4x - 2 = 98
180 - 98 = 82
Aim 3
Aim 3
Aim 3
Aim 3
CC Geometry R
Aim #3: How do we solve for unknown angles in a triangle?
Do Now:
Find the measure of angle x.
Explain your calculations.
(Hint: Draw an auxiliary line segment.)
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.
The sum of the 3 angle measures of any triangle is
degrees.
TYPES OF TRIANGLES
Type of
Triangle
Properties
• at least 2 sides are =
• at least 2 angles are =
Isosceles • If two sides are
≅, then the opposite ≮s are =.
• If two ≮s are ≅, then the opposite are =.
Scalene
• No sides are =
• No angles are =
• An equilateral Δ has all sides are =.
Equilateral • An equiangular Δ has all angles =.
• A regular triangle has =≮s and = sides.
Equiangular • If all sides of a Δ are =, all ≮s are =.
• If all ≮s of a Δare =, all sides are =.
Diagram
Solve for x in the following two triangles. a)
b)
A definition is a statement that explains the meaning of a word or term.
Example: Supplementary angles are _________________________________
A postulate is a mathematical statement accepted as true without proof.
Example: ____________________________________________________,
a pair of alternate interior angles are equal.
A theorem is a mathematical statement whose truth can be proven.
• Exterior Angle Theorem: In any triangle, the measure of the exterior angle is
equal to the sum of the measures of the _____________ or non_____________ ___________________ angles.
• Base Angles Theorem: Base angles of an _____________ triangle are equal.
• Theorem: Each angle of an equilateral triangle has a measure of ___°.
Practice:
In each figure, determine the measures of the unknown (labeled) angles. Give
reasons for your calculations.
1.
2.
m≮a = _______
3.
m≮c = _______
m≮d = _______
4.
m≮b = _____
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 40 0 , find the measure of
either of the exterior angles formed by extending the base.
9.
m≮j = _______
10.
d0
x = _______
(2x)0
(2x ­ 5)0
d = _______
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.
Date ____________________________
HW #3 (Unknown Angles in a Triangle)
Name ____________________________
CC Geometry R
1. Find the measures of angles a and b. Explain your calculations .
#2-6 In problems 2-6, determine the measures of the unknown (labeled) angles.
Give reasons for your calculations.
2.
m≮e = _____
3.
m≮k = _____
5.
4.
580
95
0
390
b
a
m≮a = _____
m≮b = _____
6.
(2x+9) 0
(3x­1) 0
m≮c = _____
c
(x+12) 0
420
7. Find the value of x:
a.
b.
x
3x­10
80o
x
25o
c.
x+15
d. Segment P is || to segment L
P
8x ­ 2
15x
L
120o
140o
x