Prove RO is Congruent to AR: Reasons Explained

[xashleyx]

yeah, sorry. I'm in a desperate bind. i have like 8 different assignments due wednesday, and i don't know how to do any of them, and my teacher in summer school couldn't help me.

Given: AF is perpendicular to AR; OG is perpendicular to RO; AO bisects FG

Prove: RO is congruent AR

Statement:

1. AF is perpendicular to AR; OG is perpendicular to RO

2. angle A and angle O are right triangles

3. triangleFAR and triangleGOR are right triangles

4. AO bisects FG (Given)

5. RG is congruent to RF

6. triangle FRA is congruent to triangle GRO

7. triangleFAR and triangleGOR are congruent

8. RO is congruent to AR

Choose the correct reasons for the statements above.

a.1. Given; 2. Definition of perpendicular lines; 3. Definition of right triangles; 5. AAS postulate; 6. Vertical angle theorem; 7. Segment bisector; 8. CPCTC

b.1. Given; 2. Definition of perpendicular lines; 3. Definition of right triangles; 5. Segment bisector; 6. Vertical angle theorem; 7. AAS postulate; 8. CPCTC

c. 1. Given; 2. Definition of vertical angles; 3. Definition of right angles; 5. AAS postulate; 6. Segment bisector; 7. Vertical angle theorem; 8. CPCTC

i said it was a.

 

[0rthodontist]

First, #6 should read angle FRA is congruent to angle GRO.

a, b, and c are the same up until #5. What does the AAS postulate say and what does it mean to say something is a segment bisector?

 

[xashleyx]

If two angles & a nonincluded side of one triangle are congruent to two angles & the corresponding nonincluded side of a second triangle, then the two triangles are congruent.

a segment that divides a line into two equal parts.

so i think this makes 5 a segment bisector.
& makes 7. aas.

sorry if I'm being really stupid.

 

[0rthodontist]

so i think this makes 5 a segment bisector.
& makes 7. aas.

Yes, that's right.

Actually in the AAS it doesn't matter whether the side is nonincluded or not--if you know 2 angles are the same between the two triangles you also know the 3rd angle is the same.

 

[xashleyx]

thank you very much.