1. It is impossible for a triangle to be which of the following?
- both isosceles and right
- both equilateral and equiangular
- both scalene and acute
- both obtuse and equilateral
2. From the markings shown on the following triangle, which of the following statements is true?
is an isosceles, right triangle.
is an equilateral, right triangle.
is an isosceles, acute triangle.
is an equiangular, acute triangle.
3. Inif
and
, then
is a scalene triangle
is an acute triangle
is a right triangle
is an isosceles triangle
4. Inif
is one inch longer than
is 10 inches shorter than the sum of
and
, and the perimeter of
is 72 inches, find the length of
.
- 20 in.
- 21 in.
- 31 in.
- 32 in.
5. If the largest angle of an isosceles triangle measures 106°, find the measure of the smallest angle.
- 37°
- 42°
- 53°
- 74°
6. In a right triangle, if one acute angle has measureand the other has measure
, find the larger of these two angles.
- 13°
- 22°
- 47°
- 68°
Use the following figure to answer questions 7-13.
7. Ifand
, find
.
- 32°
- 84°
- 94°
- 96°
8. Let, and
. Find
.
- 24°
- 58°
- 98°
- 132°
9. If, then
10. If, then
11. In order to prove thatby ASA, we would need to show that
12. If, then we can prove that
by
- SSS
- SAS
- ASA
- AAS
13. If, which of the following statements is true?
by ASA.
by SAS.
by SSA.
- We cannot prove that
.
For questions 14-20 complete the proof of Theorem 4.12 by selecting the best reason or statement.
Theorem 4.12 Medians of congruent triangles are congruent.
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14. The best statement for reason 6 of this proof is
- D is the midpoint of
.
15. The best reason for statement 7 of this proof is
- congruent angles form congruent segments
- definition of perpendicular segments
- definition of a midpoint
- reflexive property
16. The best statement for reason 10 of this proof is
- H is the midpoint of
.
17. The best reason for statement 11 of this proof is
- congruent angles form congruent segments
- definition of perpendicular segments
- definition of a midpoint
- reflexive property
18. The best reason for statement 14 of this proof is
- substitution property of equality
- definition of congruent segments
- CPCTC
- given
19. The best reason for statement 16 of this proof is
- SSS
- SAS
- ASA
- AAS
20. The best reason for statement 17 of this proof is
- substitution property of congruence
- definition of congruent segments
- CPCTC
- definition of a median
Use the following figure to answer question 21.
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21. From the construction marks shown in the diagram, we can tell thatis
- an altitude of
- an angle bisector of
- a median of
- a perpendicular bisector of


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is an isosceles, right triangle.
if
and
, then
if
is one inch longer than
is 10 inches shorter than the sum of
, and the perimeter of
and the other has measure
, find the larger of these two angles.
and
, find
.
, and
. Find
.
, then 













, then we can prove that
by
, which of the following statements is true?
by ASA.


.


.
is


