5 geometry questions.?

Question

51: For right triangle ACB with right angle C, if m Ang A = 45o and BC = 3, what is the length of AC?

3 sqrt(3)

3

3 sqrt(2)

1.5

Use Figure 2 above. If m Ang B = 53 and m Ang C = 62, which side(s) of Triangle ABC is(are) the longest?

AB

BC

AC

AB & BC

37: A polygon is regular if and only if the sides are congruent (“if and only if” states a condition but does not necessitate it to be the sole condition).

False

True

Neither

Both

38: In the proof above, the reason for step 5 is

substitution

parallel postulate

equal corresponding angles

angle addition

30: The radius of a Circle O is 4, if radii OA and OB form 90° angle, AB = ?

4 sqrt(2)

4

16 sqrt(2)

8

Figure 1: The three horizontal lines are parallel.

Figure 3: The two horizontal lines are parallel.

Figure 7: JM and JP are chords of the circle. JK is a diameter.

Figure 8: GH and JK are chords of the circle.

Use Figure 3 below for the following proof:

Given: Lines a and b are cut by the transversal f, and m ang 1 + m ang 3 = 180o.

Prove: lines a and b are parallel.

1. m ang 1 + m ang 3 = 180° : Given

2. m ang 3 + m ang 5 = 180° : Definition of straight angle

3. m ang 1 + m ang 3 = m ang 3 + m ang 5 : __________

4. m ang 1 = m ang 5 : __________

5. Lines a and b are parallel: __________

http://tinypic.com/view.php?pic=v49iu0&s=4

Answer 1

Wow, lots of questions, one at a time

51)  The triangle has a 45 degree angle and a 90 degree angle so the other angle must be 45 degrees.  That means the two legs are equal.  You know one leg (BC) is 3 so AC must = 3 as well

Next one, you know the two angles, A and C so B must be the compliment of them  C= 180-A-B = 65, which is the largest angle.  The side opposite the largest angle must be the longest.  So AB would be the longest

37, False, if and only if is a singular condition that must be met and exludes all others

38 I don't understand, must be missing info

30. You are making a triangle.  OA and OB must have lengths that are equal to the radius and  they then form a right triangle due to the degrees.  This means that AB can be had using Pythag's theorem

AB^2 = OA^2 +OB^2

AB= sq root (OA^2+OB^2)

AB= sq root (16 + 16)

AB = sq root (32)

AB = sq root (16) * sq root (2)

AB = 4 sq root (2)

Last one I'm fairly lost on what you want

Answer 2

3 because this is an isosceles right triangle

BC is the longest side because it is opposite the largest angle

37. FALSE. The angles must also be equal for regular polygon.

38. If corresponding angles are equal, the lines are ||

30. 4sqrt(2) because sqrt(4^2+4^2) = 4sqrt(2)

Answer 3

51.3

30. 8

Answer 4

51. 3 sqrt 2

BC

37. TRUE

38 parallel postulate i think.