Math 1 Unit 3 Question Set 1
Name: ________________________ Class: ___________________ Date: __________
ID: A
Math 1 Unit 3 Question Set 1 Short Answer 1. Calculate the sum of the measures of the interior angles of a regular octagon. Also, calculate the measure of each interior angle of a regular octagon. Show all your work.
9. “If Tom and Mary are classmates, then they go to the same school.” Write a statement that is logically equivalent to the statement provided.
2. The measure of each exterior angle of a regular polygon is 60. Calculate the number of sides in the polygon. Justify your reasoning.
10. If Mark passes his biology test and Philip passes his Geography test, then both of them will go to the movies. On Saturday, only Mark goes to the movies.
3. Calculate the sum of the measures of the interior angles of a regular nonagon. Also, calculate the measure of each interior angle of a regular nonagon. Show all your work.
What can you logically conclude from the above scenario?
4. The measure of each exterior angle of a regular polygon is 45. Calculate the number of sides in the polygon. Justify your reasoning.
11. What is the converse of the statement “If it is sunny, I will go swimming”?
5. How many sides does a regular polygon have if the sum of its interior angle measures is 3240?
12. The measures of two sides of a triangle are 10 and 11. Write an inequality that expresses the length of the thrid side of the triangle, m.
6. Find the measure of an interior angle and an exterior angle of a regular polygon with 45 sides.
13. What is the relationship between side AB and side AC? (Note: figure not drawn to scale)
7. Find the sum of the measures of the interior angles in the figure.
14. Is it possible for a triangle to have side lengths 3cm, 10cm, and 7cm? Justify your answer. 15. Explain why the diagonal of a square must be longer than the sides of the square.
8. Which of the following statements is/are false? [A] a quadrilateral has 6 angles [B] a hexagon has 6 angles [C] a pentagon has 5 sides [D] a hexagon has 6 sides
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Name: ________________________
ID: A
16. Elma wants to climb Miller’s Peak, but she needs to go to Sutter Spring to get water and then hike to Miller’s Peak. Will she have to hike farther than 6 mi? Explain.
21.
22.
For Questions 17 through 24, identify the exterior and remote interior angles in each triangle. Additionally, write an algebraic expression that shows the relationship between the exterior angle the remote interior angles.
23.
If possible, find the value of x. 24.
17.
18. 25. Complete the direct proof.
19.
20.
Given: m1 m4, m2 m3 Prove: mC mD
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Name: ________________________
ID: A
For the triangle shown, prove each of the following claims.
26. mABD mC 27. mABD mD 28. Prove using The Side-Side-Side Postulate that Triangle ABC is congruent to Triangle DEF
29. Given: Point E is the midpoint of segments AB and CD. Prove: Triangle AED is congruent to Triangle BEC
30. Given: BA MA,B M Prove: BAT MAN
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ID: A
Math 1 Unit 3 Question Set 1 Short Answer 1. Calculate the sum of the measures of the interior angles of a regular octagon. Also, calculate the measure of each interior angle of a regular octagon. Show all your work.
9. “If Tom and Mary are classmates, then they go to the same school.” Write a statement that is logically equivalent to the statement provided.
2. The measure of each exterior angle of a regular polygon is 60. Calculate the number of sides in the polygon. Justify your reasoning.
10. If Mark passes his biology test and Philip passes his Geography test, then both of them will go to the movies. On Saturday, only Mark goes to the movies.
3. Calculate the sum of the measures of the interior angles of a regular nonagon. Also, calculate the measure of each interior angle of a regular nonagon. Show all your work.
What can you logically conclude from the above scenario?
4. The measure of each exterior angle of a regular polygon is 45. Calculate the number of sides in the polygon. Justify your reasoning.
11. What is the converse of the statement “If it is sunny, I will go swimming”?
5. How many sides does a regular polygon have if the sum of its interior angle measures is 3240?
12. The measures of two sides of a triangle are 10 and 11. Write an inequality that expresses the length of the thrid side of the triangle, m.
6. Find the measure of an interior angle and an exterior angle of a regular polygon with 45 sides.
13. What is the relationship between side AB and side AC? (Note: figure not drawn to scale)
7. Find the sum of the measures of the interior angles in the figure.
14. Is it possible for a triangle to have side lengths 3cm, 10cm, and 7cm? Justify your answer. 15. Explain why the diagonal of a square must be longer than the sides of the square.
8. Which of the following statements is/are false? [A] a quadrilateral has 6 angles [B] a hexagon has 6 angles [C] a pentagon has 5 sides [D] a hexagon has 6 sides
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Name: ________________________
ID: A
16. Elma wants to climb Miller’s Peak, but she needs to go to Sutter Spring to get water and then hike to Miller’s Peak. Will she have to hike farther than 6 mi? Explain.
21.
22.
For Questions 17 through 24, identify the exterior and remote interior angles in each triangle. Additionally, write an algebraic expression that shows the relationship between the exterior angle the remote interior angles.
23.
If possible, find the value of x. 24.
17.
18. 25. Complete the direct proof.
19.
20.
Given: m1 m4, m2 m3 Prove: mC mD
2
Name: ________________________
ID: A
For the triangle shown, prove each of the following claims.
26. mABD mC 27. mABD mD 28. Prove using The Side-Side-Side Postulate that Triangle ABC is congruent to Triangle DEF
29. Given: Point E is the midpoint of segments AB and CD. Prove: Triangle AED is congruent to Triangle BEC
30. Given: BA MA,B M Prove: BAT MAN
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