Download Transversals_and_Triangle_sum_proof

Name: ________________________
Geometry – Mr. Lewis
Date: __________________________
What can parallel lines and linear pairs tell us?
Directions:
 Copy the diagram above into your notebook or graph paper.
 Use up as much space as possible, Label the points EXACTLY AS SHOWN!
 Use the lines on your paper to make sure that AB is parallel to CD.
Given: ⃡𝐴𝐵 ∥ ⃡CD (This statement says Line AB is parallel to Line CD)
1. Use your protractor to measure ∠ GEB and ∠ EFD
a. m∠ GEB = ______°
b. m ∠ EFI = ______°
2. Is this the result that was expected?
3. What is this type of angle pair called?
4. Use linear pairs to find the remaining angles without your protractor!
a. m∠ FEA = ______°
c. m∠ HFI = ______°
b. m∠ HFC = ______°
d. m∠ EFC = ______°
5. All the acute angles in this diagram are congruent.
True
False
6. All the obtuse angles in this diagram are congruent.
True
False
Name: ________________________
Geometry – Mr. Lewis
Date: __________________________
Proof of the Triangle Sum Theorem
Using the same diagram from page 1, Use a ruler to connect points E and I. Extend this line as
far as possible.
7. Use a protractor to find the measure of ∠ BEI. __________
8. Angles ∠ FEA, ∠ FEI, and ∠ BEI are (choose one)
a) Complementary b) Vertical
c) Supplementary
d) Alternate exterior
9. m ∠ EIF = m ∠ BEI
(Explain your choice)
True
False
10. Determine, without a protractor, the measure of ∠ FEI. _________
Explain your reasoning.
11. Fill in the blanks.
m∠ EFI = _____°
m∠ FEI = ____°
m∠ EIF = ______°
12. Does triangle EFI follow the “Triangle Sum Theorem”? Explain.
Statement – Reason Practice
13. Write a statement – reason proof that shows the value of all angles 1-12. Be sure to use proper
vocabulary.
Ex:
Statement
Reason
∠ 1 = 120°
Vertical Angles are congruent.
∠ 2 = 60°
Supplementary Angles add up to 180°
Continue….
Name: ________________________
Geometry – Mr. Lewis
Date: __________________________
Midpoint, Mid-segment and Side-splitter Theorem
Directions: Copy the diagram above into your notebooks. Answer the questions below. If you
choose TRUE as an answer, name the theorem that makes your answer true.
Given: Segment FE is the mid-segment of triangle ABC. Point D is the midpoint of BC
14. Point F is the midpoint of AB.
True
False
15. FE = BD
True
False
16. AE = FB
True
False
17. FE ∥BC (Parallel)
True
False
18. Name two pairs of congruent angles in the image above.
Given: m∠ FAE = 75° and m∠ FEC = 120°
19. Use the “Exterior Angle Theorem” and the given information to determine m∠ AFE.
20. Find the measure of the remaining angles, justify each answer.
m∠AEF = _____°
m∠BFE = _____°
m∠ECB = _____°
m∠FBD = _____°
Given: AF = 5.6 ft., EC = 4.5 ft., and BC = 12.5 ft. Label all missing measurements.
21. Find the perimeter of Triangle AFE (SHOW ALL STEPS)
22. Find the perimeter of Quadrilateral BFEC. (SHOW ALL STEPS)