Download Louis Pasteur Middle School 67 8th Grade Mathematics Mr

Louis Pasteur Middle School 67
8th Grade Mathematics
Mr. Wieckhorst
Test Outline: Angle Relationships and Triangles
Test Date: Friday, October 5th, 2012
Test Format: The test will be scored out of 25 points.
Part I: Multiple Choice (10 questions, 1 point each)
Part II: Short/Extended Response (5 questions, 15 total points)
Test Topics:
- Complementary Angles
- Supplementary Angles
- Vertical Angles
- Parallel Lines Cut by a Transversal (know the vocabulary and how to find
missing angle measurements)
- Finding a missing side in similar triangles
- Proving that two triangles are similar
- Triangle Angle Sum Theorem
- Exterior Angles of Triangles
- Proving the Triangle Angle Sum Theorem using Parallel Lines Cut by a
Transversal
- Equations with Angles and Using Substitution to find the angle
measurement after solving for “x”.
Please read and review this outline, study your notes from 9/24 to 10/4, and try the
attached review sheet. Once you have completed the review sheet, you may check
your answers on the page after the questions.
Please cut out and sign the bottom portion of this page. They will be collected on the
day of the test.
-----------------------------------------------------------------------------------------------------------8th Grade Angle Relationships and Triangles
Student Name: _____________________________________________________________
Class: ______________
Parent/Guardian Signature: __________________________________________________
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Review Sheet
Angle Relationships and Triangles
1.
a. What are “complementary” angles?
b. An angle measures 25 degrees. What is the measure of its complement?
c. Angle A and B are complementary. Angle A measures 5x + 2. Angle B
measures 13x – 2. What is the measure of Angle A?
d. Name an angle complementary to angle EPC.
2.
a. Name an angle supplementary to GPE
b. An angle measures 108 degrees. What is the measure of its supplement?
c. B = 10x and A = 7x – 7. What is m<B?
3. If angle 2 measures 67 degrees, find the measures of the other three angles
4.
a. From the picture below, give an example of each of the following:
- Corresponding Angles
- Alternate Interior Angles
- Alternate Exterior Angles
- Same Side Interior Angles
- Same Side Exterior Angles
b. In the picture above, m<4 = 10x – 17 and m<8 = 8x + 11. Find the value of x
and the measure of angle 4.
c. Explain why you made the equation you used to solve part b.
5. Find the length of side AC.
6. Draw any two triangles that are “similar”. Explain, in detail, what makes these
triangles similar.
7. In Triangle ABC, A = 4x, B = 5x – 13, and C = 3x + 13. Find the measure of each
angle.
8. True or false: The sum of the exterior angles of a triangle is 360 degrees.
9. Find the value of x.
10. Write a two column proof that shows that m<1 + m<2 + m<3 = 180.
Answers:
1.
a. Complementary angles are any two angles whose sum is 90 degrees. That
means that when you place them together, a right angle is formed.
b. 65 degrees
c. x = 5; m<A = 63 degrees
d. Angle CPG or Angle FPH (because vertical angles are congruent)
2.
a. Angle FPE
b. 72 degrees
c. x = 1; B = 110 degrees
3. Angle 4 measures 67 degrees (because all vertical angles are congruent). Angles 1
and 3 measure 113 degrees because they are supplementary to 2 and 4, and they
are also vertical to each other.
4.
a.
- Corresponding Angles (1 and 5, 2 and 6, 3 and 7, 4 and 8)
- Alternate Interior Angles (3 and 6, 4 and 5)
- Alternate Exterior Angles (1 and 8, 2 and 7)
- Same Side Interior Angles (3 and 5, 4 and 6)
- Same Side Exterior Angles (1 and 7, 2 and 8)
b. x = 14; m<4 = 123 degrees
c. The equation used was 10x – 17 = 8x + 11. They were set equal to each
other because angles 4 and 8 are corresponding angles, therefore congruent.
5. AC = 7.5 cm
6. (answers may vary)- Similar triangles are any two triangles that meet the
following conditions: Their corresponding interior angles are congruent, and their
corresponding sides are in proportion. Similar triangles can be achieved by
dilations.
7. x = 15; m<A = 60, m<B = 62, m<C = 58
8. True. Also, if you take the sum of the exterior angles of a triangle and subtract the
sum of the interior angles, you will always get 180 degrees.
9. 100 degrees
10. Proof is in paragraph form
m<3 + m<4 + m<5 = 180 because of the definition of supplementary angles.
Line m is parallel to side BC (given). Angle 4 is congruent to Angle 1 because they
are alternate interior angles. Angle 5 is congruent to Angle 2 because they are
alternate interior angles. m<1 + m<2 + m<3 = 180 by the Substitution Property.