1 Honors GST Chapter 5 Study Guide 1. Solve for x
Honors GST Chapter 5 Study Guide
1. Solve for x. Then give the measures of the three interior angles of the triangle, and the exterior angle of the triangle.
X= Interior ∠1: _____________
Interior ∠2: _____________
Exterior Angle: _________________
2. List all corresponding congruent parts of the congruent pentagons, and then write a different true congruence statement:
Congruent Statement: Congruent Sides:
Congruent Angles:
3. Find the value of the following angles: m∠NCA =
m∠BND =
m∠ANC =
m∠BDN =
m∠ACD =
m∠CND =
4. Is the following figure stable? Explain why or why not.
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Interior ∠3: _______________
5. Are the following statements true or false? If true, explain. ∠FGJ ≅∠JML. FJ ≅HK FJ≅HG ∠FGJ ≅∠HGK JM ≅ GK
6. Solve for x, then solve for each acute angle: X= Acute angles: __________0 and ___________0
7. Complete the following statements: If AE≅ED, then ∠________ ≅ ∠_________ If BE≅CE, then ∠________ ≅ ∠_________
8. Suppose G is the midpoint of EH. Is FE ≅HI? Explain
9. Using the diagram, how would you find the distance across the canyon (DE) without actually crossing or measuring? Explain.
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10. You have a triangle with A(0,0), B(4,6), and C (___, 0) What is the x coordinate that would make this an isosceles triangle? (Hint: Graph it!)
USE THE FOLLOWING TO ANSWER 11 - 13 11. Name all triangles that are isosceles.
12. Name all triangles that are equilateral.
13. Find the measures of the following angles: m∠BAC =
m∠EAF =
m∠CAD =
m∠FAG =
m∠DAE =
14. Find the length of BC.
15 In the diagram with a tree, JL≅LM. What theorem would be used to prove that ΔJKL ≅ ΔMKL.
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16. What is the value of x?
17. A boat is traveling parallel to the shore along RT. When the boat at point R, the captain measures the angle to the lighthouse as 350. After the boat travels 2.1 miles, the captain measures the angle to the lighthouse to be 700.
What is the measure of SL? Explain.
18. The measure of ML is 8. The measure of MK is 5x+3, and the measure of MJ is 3x+y.
Solve for x and y.
19. A ramp is designed as a right triangle. One of the acute angles is twice the sum of the other acute angle and 30. What is the measure of each acute angle?
20. ΔABC ≅ ΔDEF
Find the value of x and y.
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20. In a right triangle, the sum of 3 times one acute angle and 4 times the other angle is equal to 3150. What is the measure of both acute angles?
21.
22.
23.
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1. Solve for x. Then give the measures of the three interior angles of the triangle, and the exterior angle of the triangle.
X= Interior ∠1: _____________
Interior ∠2: _____________
Exterior Angle: _________________
2. List all corresponding congruent parts of the congruent pentagons, and then write a different true congruence statement:
Congruent Statement: Congruent Sides:
Congruent Angles:
3. Find the value of the following angles: m∠NCA =
m∠BND =
m∠ANC =
m∠BDN =
m∠ACD =
m∠CND =
4. Is the following figure stable? Explain why or why not.
1
Interior ∠3: _______________
5. Are the following statements true or false? If true, explain. ∠FGJ ≅∠JML. FJ ≅HK FJ≅HG ∠FGJ ≅∠HGK JM ≅ GK
6. Solve for x, then solve for each acute angle: X= Acute angles: __________0 and ___________0
7. Complete the following statements: If AE≅ED, then ∠________ ≅ ∠_________ If BE≅CE, then ∠________ ≅ ∠_________
8. Suppose G is the midpoint of EH. Is FE ≅HI? Explain
9. Using the diagram, how would you find the distance across the canyon (DE) without actually crossing or measuring? Explain.
2
10. You have a triangle with A(0,0), B(4,6), and C (___, 0) What is the x coordinate that would make this an isosceles triangle? (Hint: Graph it!)
USE THE FOLLOWING TO ANSWER 11 - 13 11. Name all triangles that are isosceles.
12. Name all triangles that are equilateral.
13. Find the measures of the following angles: m∠BAC =
m∠EAF =
m∠CAD =
m∠FAG =
m∠DAE =
14. Find the length of BC.
15 In the diagram with a tree, JL≅LM. What theorem would be used to prove that ΔJKL ≅ ΔMKL.
3
16. What is the value of x?
17. A boat is traveling parallel to the shore along RT. When the boat at point R, the captain measures the angle to the lighthouse as 350. After the boat travels 2.1 miles, the captain measures the angle to the lighthouse to be 700.
What is the measure of SL? Explain.
18. The measure of ML is 8. The measure of MK is 5x+3, and the measure of MJ is 3x+y.
Solve for x and y.
19. A ramp is designed as a right triangle. One of the acute angles is twice the sum of the other acute angle and 30. What is the measure of each acute angle?
20. ΔABC ≅ ΔDEF
Find the value of x and y.
4
20. In a right triangle, the sum of 3 times one acute angle and 4 times the other angle is equal to 3150. What is the measure of both acute angles?
21.
22.
23.
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