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**Triangle Practice Test**

**Directions:** A good score is eight correct.

1. Suppose there are three triangles, called Δ *ABC* , Δ *DEF* , and Δ *PQR* . If Δ *ABC* ≅ Δ *DEF* and Δ *DEF* ≅ Δ *PQR* , we can surmise that Δ *ABC* and Δ *PQR* are

(a) directly congruent

(b) directly similar, but not directly congruent

(c) inversely congruent

(d) not related in any particular way

2. Suppose there are two triangles, called Δ *ABC* and Δ *DEF* . If these two triangles are directly similar, then we can be certain that

(a) ∠ *ABC* and ∠ *DFE* have equal measure

(b) ∠ *BCA* and ∠ *EFD* have equal measure

(c) ∠ *CAB* and ∠ *FED* have equal measure

(d) both triangles are equilateral

3. Suppose a given triangle is directly congruent to its mirror image. We can be absolutely certain that this triangle is

(a) equilateral

(b) isosceles

(c) acute

(d) obtuse

4. Suppose a triangle has sides of lengths *s, t* , and *u* , in centimeters (cm). Which of the following situations represents a right triangle? Assume the lengths are mathematically exact (no measurement error).

(a) *s* = 2 cm, *t* = 3 cm, *u* = 4 cm

(b) *s* = 4 cm, *t* = 5 cm, *u* = 7 cm

(c) *s* = 6 cm, *t* = 8 cm, *u* = 10 cm

(d) *s* = 7 cm, *t* = 11 cm, *u* = 13 cm

5. Suppose there are two triangles, called Δ *ABC* and Δ *DEF* . Also suppose that side *DE* is twice as long as side *AB* , side *EF* is twice as long as side *BC* , and side *DF* is twice as long as side *AC* . Which of the following statements is true?

(a) The interior area of Δ *DEF* is twice the interior area of Δ *ABC*

(b) The perimeter of Δ *DEF* is four times the perimeter of Δ *ABC*

(c) The interior area of Δ *DEF* is four times the interior area of Δ *ABC*

(d) Δ *ABC* ≅ Δ *DEF*

6. Suppose a triangle has a base length of 4 feet and a height of 4 feet. Its interior area is

(a) 4 square feet

(b) 8 square feet

(c) 16 square feet

(d) impossible to determine without more information

7. The perimeter of the triangle described in the previous question is

(a) 8 feet

(b) 16 feet

(c) 22 feet

(d) impossible to determine without more information

8. Draw a triangle on a piece of paper. Label the vertices {, [, and (, proceeding in a counterclockwise sense. Look at this figure and call it Δ {[(. Now hold the piece of paper between your eyes and a bright light, and turn the inked side away from you but keep the page right-side-up. You should see a figure that you can call Δ)]}, because the vertices appear as), ], and } in a counterclockwise sense. Which of the following statements is true?

(a) These two triangles are directly congruent

(b) These two triangles are directly similar, but not directly congruent

(c) These two triangles are inversely congruent

(d) These two triangles are inversely similar, but not inversely congruent

9. Take the same piece of paper that you used in the preceding problem. Look at Δ{[(. Now turn the paper upside down, keeping the inked side facing you. You should see another triangle that you can call Δ}]) as the vertices appear in a counterclockwise sense. Which of the following statements is true?

(a) These two triangles are directly congruent

(b) These two triangles are directly similar, but not directly congruent

(c) These two triangles are inversely congruent

(d) These two triangles are inversely similar, but not inversely congruent

10. Suppose there is a triangle, two of the interior angles of which measure 30°. The measure of the third angle is

(a) impossible to determine without more information

(b) π/6 rad

(c) π/4 rad

(d) 2π/3 rad

**Answers:**

1. a

2. b

3. b

4. c

5. c

6. b

7. d

8. c

9. a

10. d

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