Lines and Transversals
Geometric Proofs
Angles of Triangles
Angles and Polygons
Vocabulary
100
Use the figure on the board to answer the following question. 


Angles 2 and 6 are examples of what?

Corresponding angles
100
In the figure on the board, two lines intersect to form four angles.  If the measure of angle 7 = 9x and the measure of angle 8 = 11x, complete the following paragraph proof to show that x = 9.

Given:  Two intersecting lines with the measure of angle 7= 9x and the measure of angle 8 = 11x.

Prove:  x = 9

Proof:  Angles 7 and 8 form a __________ angle so they are _____________ angles.
straight; supplementary.
100
Two interior angles of a triangle are 62 and 65 degrees respectively.  What is the measure of the other angle?

53 degrees

100
Find the sum of the measures of the interior angles of a 13-gon.
1,980 degrees.
100
What are angles that are in the same position on the two lines in relation to the transversal called?
Corresponding angles
200

Use the figure on the board to answer the following question. 



Angles 1 and 8 are examples of what?

Exterior angles
200

In the figure on the board, two lines intersect to form four angles. If the measure of angle 7 = 9x and the measure of angle 8 = 11x, complete the following paragraph proof to show that x = 9.


Given: Two intersecting lines with the measure of angle 7= 9x and the measure of angle 8 = 11x.


Prove: x = 9


Proof: So the measure of angle 7 + the measure of angle 8  = _______ degrees, by the definition of supplementary angles.

180 
200

Two interior angles of a triangle are 79 and 55 degrees respectively. What is the measure of the other angle?

46 degrees

200
A quilt pattern is made of repeating equilateral triangles.  What is the measure of one interior angle of an equilateral triangle?
60 degrees
200
What is a statement or conjecture that has been proven and can be used as a reason to justify statements in other proofs called?
A theorem
300
What is the angle that is corresponding to angle 8?
Angle 4
300

In the figure on the board, two lines intersect to form four angles. If the measure of angle 7 = 9x and the measure of angle 8 = 11x, complete the following paragraph proof to show that x = 9.


Given: Two intersecting lines with the measure of angle 7= 9x and the measure of angle 8 = 11x.


Prove: x = 9


Proof: By substitution, ____ + 11x = 180.  So, x = 9 by the ___________ Property of Equality.

9x; Division
300
Refer to the diagram on the board. Find the value of x in the triangle.
112 degrees
300
Find the measure of an exterior angle of a regular pentagon.
72 degrees
300
What uses facts, rules, definitions, or laws to make conjectures from given situations?
Deductive reasoning
400

If lines m and n are parallel, then angles 3 and ____ have equal measures.

Angle 6
400
Describe the theorem or definition you could use to find the measure of angle 2 in the diagram on the board.
Vertical angles have the same measure.
400

The measures of the angles of triangle XYZ are in the ratio 3:3:6.  What are the measures of the angles?

45 degrees, 45 degrees, and 90 degrees
400
A stained glass window is in the shape of a regular hexagon.  What is the measure, in degrees, of an interior angle in the window?
120 degrees
400
What is a polygon that is equilateral and equiangular called?
A regular polygon
500
Refer to the figure of the building on the board.  Parallel lines are cut by a transversal.  If the measure of angle 1 = 86 degrees, find the measure of angles 2 and 3.
The measure of angle 2 is 94 degrees.  The measure of angle 3 is 86 degrees.
500
Given the right triangles shown on the board, use inductive reasoning to make a conjecture about the sum of the measures of the two acute interior angles of any right triangle.
The sum of the measures of the acute interior angles of a right triangle is 90 degrees.  So, the acute interior angles are complementary.
500
In triangle ABC the measure of angle A is 2x + 3, the measure of angle B is 4x + 2, and the measure of angle C is 2x - 1.  What are the measures of the angles?
Angle A is 47 degrees.

Angle B is 90 degrees. 

Angle C is 43 degrees.

500
A designer is creating a new logo for a bank.  The logo consists of a regular pentagon surrounded by isosceles triangles.  Find the measure of an interior angle of a regular pentagon.
108 degrees
500
What are interior angles that lie on opposite sides of the transversal called?
Alternate interior angles
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