Potomac Falls High School Author: LCPS Last modified by: Carly Fabris Created Date: 1/13/2016 5:04:00 PM Company: LCPS Other titles: Potomac Falls High School ...

| Part I. Fill in the | |blank. |

1. In a triangle, the smallest angle is across from __________________________________________. 2. _____, _____, _____, _____, _____ are the five methods to prove triangles congruent. 4. Equiangular triangles are also ________________________________. 5. Corresponding parts of congruent triangles are _______________________________. 7. The hypotenuse of a right triangle is opposite the ____________________________________. 8. If two sides of a triangle have length 4 and 6 then the third side must be between ____ and ____.

Fill in the blank with Always, Sometimes, or Never. 1. Isosceles triangles are acute. _____ 2. An acute triangle is equilateral. _____ 3. A scalene triangle is obtuse. _____ 4. A right triangle is isosceles. _____

Find the value of x. 5. 6.

Determine which postulate or theorem can be used to prove the triangles are congruent. 7. 8. 9.

Find the value of x and y. 10. 11. 12.

13. What is the vertex of [pic]ABC? __________

Write the inequality relating each pair of measures. 1. m[pic]PRQ _______ m[pic]PRS 2. m[pic]DBC ________ m[pic]ABE

3. Use the figure to the right to write an inequality to describe the possible values of x.

4. The measures of the angles in a triangle are in the extended ratio 1:4:7. Find the measures of the angles. _____ _____ _____

Solve each proportion. Find the geometric mean of the two numbers. 5. [pic] 6. 3 and 27

7. Given that [pic]use the diagram to find the values of x and y.

17. Luke Skywalker is 5 feet 9 inches tall. He casts a shadow that is 3 feet 4 inches long. R2D2 casts a shadow that is 28 inches long. How tall is R2D2? C3PO is 69 inches tall. How long is his shadow?

8. The dotted segment is a special segment in similar triangles. Find the value of the variable.

Find the value of the variable. 9. 10.

Part III. Proofs

Complete each proof.

2. GIVEN: [pic] M is the midpoint of [pic]

PROVE: [pic]

| Statements | Reasons | |1. |1. Given | |2. M is the midpoint of [pic] |2. | |3. |3. Definition of a midpoint | |4. |4. Reflexive property | |5. |5. SSS | |6. [pic] |6. |

Complete the following proof. (not drawn to scale)

GIVEN: GK = 2 GJ = 30 GF = 6 FH = 4

PROVE: [pic]

[pic] | Statements | Reasons | |1. |1. Given | |2. GJ = 30 |2. | |3. GF = 6 |3. | |3. |4. Given | |4. GF + FH = GH |5. | |6. |6. Substitution Property | |7. |7. Combine like terms | |8. [pic] |8. | |9. [pic] |9. | |10. [pic] |10. | |11. [pic]≅[pic] |11. Reflexive Property |

12. [pic] 12.

| Part I. Fill in the | |blank. |

1. In a triangle, the smallest angle is across from __________________________________________. 2. _____, _____, _____, _____, _____ are the five methods to prove triangles congruent. 4. Equiangular triangles are also ________________________________. 5. Corresponding parts of congruent triangles are _______________________________. 7. The hypotenuse of a right triangle is opposite the ____________________________________. 8. If two sides of a triangle have length 4 and 6 then the third side must be between ____ and ____.

Fill in the blank with Always, Sometimes, or Never. 1. Isosceles triangles are acute. _____ 2. An acute triangle is equilateral. _____ 3. A scalene triangle is obtuse. _____ 4. A right triangle is isosceles. _____

Find the value of x. 5. 6.

Determine which postulate or theorem can be used to prove the triangles are congruent. 7. 8. 9.

Find the value of x and y. 10. 11. 12.

13. What is the vertex of [pic]ABC? __________

Write the inequality relating each pair of measures. 1. m[pic]PRQ _______ m[pic]PRS 2. m[pic]DBC ________ m[pic]ABE

3. Use the figure to the right to write an inequality to describe the possible values of x.

4. The measures of the angles in a triangle are in the extended ratio 1:4:7. Find the measures of the angles. _____ _____ _____

Solve each proportion. Find the geometric mean of the two numbers. 5. [pic] 6. 3 and 27

7. Given that [pic]use the diagram to find the values of x and y.

17. Luke Skywalker is 5 feet 9 inches tall. He casts a shadow that is 3 feet 4 inches long. R2D2 casts a shadow that is 28 inches long. How tall is R2D2? C3PO is 69 inches tall. How long is his shadow?

8. The dotted segment is a special segment in similar triangles. Find the value of the variable.

Find the value of the variable. 9. 10.

Part III. Proofs

Complete each proof.

2. GIVEN: [pic] M is the midpoint of [pic]

PROVE: [pic]

| Statements | Reasons | |1. |1. Given | |2. M is the midpoint of [pic] |2. | |3. |3. Definition of a midpoint | |4. |4. Reflexive property | |5. |5. SSS | |6. [pic] |6. |

Complete the following proof. (not drawn to scale)

GIVEN: GK = 2 GJ = 30 GF = 6 FH = 4

PROVE: [pic]

[pic] | Statements | Reasons | |1. |1. Given | |2. GJ = 30 |2. | |3. GF = 6 |3. | |3. |4. Given | |4. GF + FH = GH |5. | |6. |6. Substitution Property | |7. |7. Combine like terms | |8. [pic] |8. | |9. [pic] |9. | |10. [pic] |10. | |11. [pic]≅[pic] |11. Reflexive Property |

12. [pic] 12.