Math Help Forum: Triangles.

1. It is impossible for a triangle to be which of the following?

1. both isosceles and right
2. both equilateral and equiangular
3. both scalene and acute
4. both obtuse and equilateral

2. From the markings shown on the following triangle, which of the following statements is true?

1. is an isosceles, right triangle.
2. is an equilateral, right triangle.
3. is an isosceles, acute triangle.
4. is an equiangular, acute triangle.

3. In if and , then

1. is a scalene triangle
2. is an acute triangle
3. is a right triangle
4. is an isosceles triangle

4. In if 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 .

1. 20 in.
2. 21 in.
3. 31 in.
4. 32 in.

5. If the largest angle of an isosceles triangle measures 106°, find the measure of the smallest angle.

1. 37°
2. 42°
3. 53°
4. 74°

6. In a right triangle, if one acute angle has measure and the other has measure , find the larger of these two angles.

1. 13°
2. 22°
3. 47°
4. 68°

Use the following figure to answer questions 7-13.

7. If and , find .

1. 32°
2. 84°
3. 94°
4. 96°

8. Let , and . Find .

1. 24°
2. 58°
3. 98°
4. 132°

9. If , then

1. 
2. 
3. 
4. 

10. If , then

1. 
2. 
3. 
4. 

11. In order to prove that by ASA, we would need to show that

1. 
2. 
3. 
4. 

12. If , then we can prove that by

1. SSS
2. SAS
3. ASA
4. AAS

13. If , which of the following statements is true?

1. by ASA.
2. by SAS.
3. by SSA.
4. 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.


14. The best statement for reason 6 of this proof is

1. 
2. 
3. D is the midpoint of .
4. 

15. The best reason for statement 7 of this proof is

1. congruent angles form congruent segments
2. definition of perpendicular segments
3. definition of a midpoint
4. reflexive property

16. The best statement for reason 10 of this proof is

1. 
2. 
3. H is the midpoint of .
4. 

17. The best reason for statement 11 of this proof is

1. congruent angles form congruent segments
2. definition of perpendicular segments
3. definition of a midpoint
4. reflexive property

18. The best reason for statement 14 of this proof is

1. substitution property of equality
2. definition of congruent segments
3. CPCTC
4. given

19. The best reason for statement 16 of this proof is

1. SSS
2. SAS
3. ASA
4. AAS

20. The best reason for statement 17 of this proof is

1. substitution property of congruence
2. definition of congruent segments
3. CPCTC
4. definition of a median

Use the following figure to answer question 21.

21. From the construction marks shown in the diagram, we can tell that is

1. an altitude of
2. an angle bisector of
3. a median of
4. a perpendicular bisector of

Hello,

This is a lot...

Where do you have difficulties ?

Originally Posted by Moo

Hello,

This is a lot...

Where do you have difficulties ?

3, 8, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21.

Originally Posted by ChristieZissler

3. In if and , then

1. is a scalene triangle
2. is an acute triangle
3. is a right triangle
4. is an isosceles triangle

The sum of the interior angles of any triangle is 180 degrees. So what is the measure of angle O?

Does this triangle contain an obtuse angle? A right angle? Are any of the angle measures equal?

-Dan

Originally Posted by ChristieZissler

8. Let , and . Find .

1. 24°
2. 58°
3. 98°
4. 132°

Well, angle EBA, angle EBD, and angle DBC are all part of a straight angle. So angle EBA + angle EBD + angle DBC = 180 degrees. That will give you x. So now you know two angles of triangle BCD. How do you find the third angle of this?

-Dan

What does m< represent ? (in 8.)

Originally Posted by ChristieZissler

Use the following figure to answer questions 7-13.

11. In order to prove that by ASA, we would need to show that

1. 
2. 
3. 
4. 

Give this one another try. It's a definition. ASA means angle-side-angle. Angles EBA and DBC are equal, sides AB and CB are equal, so we would need to know what more to prove these congruent by ASA?

-Dan

Originally Posted by Moo

What does m< represent ? (in 8.)

m<A stands for the "measure of angle A."

-Dan

Originally Posted by ChristieZissler

21. From the construction marks shown in the diagram, we can tell that is

1. an altitude of
2. an angle bisector of
3. a median of
4. a perpendicular bisector of

This is the basic construction for an angle bisector...

Construction: Bisect Angle