Are the triangles below similar? Explain how you know.
Yes. Explanations will vary.
Angles are 65, 65, and 50 degrees.
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3x Points
Alternate Exterior Angles
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5x Points
Corresponding Angles
Use the diagram to write and solve an equation to find angle BAG and angle CGA.
10x - 100 + 3x + 7 = 180
13x -93 = 180
13x = 273
x = 21 degrees
angle BAT = 70 degrees
angle
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4x points
Same-Side Interior Angles
Find the m∠A and m∠B. Show your work.
x = 11
angle B = 75
angle A = 50
angle C = 55
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2x points
Remote Interior Angles
Name all angles that are congruent to angle 1
Angle 4 (vertical angles are congruent)
Angle 5 (corresponding angles are congruent)
Angle 8 (alternate exterior angles are congruent)
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3x Points
Exterior Angle
How many exterior angles does a triangle have?
6
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Supplementary Angles
Use the diagram and the fact that m∠2 = 70° to find the angle measures of ∠3. Identify and explain the angle relation you use to solve.
anlge 3 = 180 - angle 2
angle 3 = 180 - 70
angle 3 = 110
True or False. Similar triangles must have congruent angles and congruent sides.
Explain your reasoning.
False. Similar triangles must have congruent angles and proportional sides.
If the m∠4 = 55° and the m∠3 = 60°, find the measures of ∠1 and ∠2.
Angle 1 = 55 + 60 = 115
Angle 2 = 180 - 115 = 65
Name one set of alternate exterior angles
Name one set of same-side interior angles
Name one set of alternate interior angles
Name one set of corresponding angles
Alternate exterior angles:
angle 1 and 8
angle 2 and 7
Same-side interior angles
angle 3 and 5
angle 4 and 6
Alternate interior angles
angle 4 and 5
angle 3 and 6
Corresponding angles
angles 1 adn 5
angles 3 and 7
angles 2 and 6
angles 4 and 8
What is the triangle sum theorem?
m<a + m<b + m<c = 180 degrees
Use the diagram and the fact that m∠2 = 50° to find the angle measures of ∠1. Identify and explain the angle relation you use to solve.
angle 1 and angle 2 are alternate interior angles, which are congruent so angle 1 also equals 50 degrees
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2x Points
Alternate Interior Angles
Use the diagram to write and solve an equation to find angle BAG and angle CGA.
Same side interior angles equal 180 degrees.
3x + 7 + 10 x -100 = 180
13x - 93 = 180
13x = 273
x = 21
angle BAG = 3(21) + 7 = 70 degrees
angle CGA = 110 degrees
Doritos is testing a new product - Jumbo-ritos. The original size and big size are similar. Use the figure below to determine the height of the big chip.
6.25 inches
Are triangles ADE and ABC similar? Explain how you know.
Yes. The triangles share angle DAE and angle BAC. Lines DE and lines BC are parallel lines. Angles ADE and angles ABC are corresponding angles of the parallel lines, which means their congruent.
What is the value of x?
116 degrees
What is the measure of x?
9 inches
20 feet
The diagram shows the shadows cast by a signpost and a flagpole. How tall is the flagpole?
20 feet