Question

Can someone please check this?


Line segment BD is congruent to line segment CD. I think that the reason for this is the Partition Postulate. Am I correct?

Answer 1

is there more to this question?

Answer 2

Yes, just a moment.

Answer 3

Given: Line segment AB is congruent to line segment AC, angle BAD is congruent to CAD

Prove: line segment AD bisects line segment BC

Answer 4

Statements:
1. line segment AB is congruent to line segment AC
2. angle BAD is congruent to angle CAD
3. line segment AD is congruent to line segment AD
4. Triangle BAD is congruent to triangle CAD
5. line segment BD is congruent to line segment CD
6. Line segment AD bisects line segment BC

Reasons:
1. Given
2. Given
3. Reflexive Property
4. ???
5. ???
6. Definition of Segment Bisector

Answer 5

That's everything.

Answer 6

They want the reason for statement 4:

4 . Triangles are congruent.

What ways do you know to show 2 triangles are congruent?

now look at statements 1,2,3 what do they say?

Answer 7

1. line segment AB is congruent to line segment AC
2. angle BAD is congruent to angle CAD
3. line segment AD is congruent to line segment AD

Answer 8

"What ways do you know to show 2 triangles are congruent?"
By using tick marks or the half circle symbol.

Answer 9

line segment (also known as) a SIDE of the triangle

Answer 10

See http://www.regentsprep.org/Regents/math/geometry/GPB/theorems.htm
You prove triangles are congruent by (1) SSS (2) SAS (3) ASA (4) AAS

Answer 11

The first 3 statements are helpful to using one of those 4. Which one?

Answer 12

I'd say the second one perhaps.

Answer 13

there is no perhaps
1. line segment AB is congruent to line segment AC <--- means SIDE = SIDE
2. angle BAD is congruent to angle CAD <--- means ANGLE = ANGLE
3. line segment AD is congruent to line segment AD <--- means SIDE = SIDE

Answer 14

I understand.

Answer 15

once you show SAS in that order, you have proven the triangles are congruent.

Reason 4:
SAS

Answer 16

I understand what you mean.
Am I correct for the fifth reason?

Answer 17

The whole reason you prove the triangles are congruent is so you can claim some part of them are congruent, in this case their "bottom" leg

Answer 18

If you know 2 triangles are congruent then you know the "parts" that correspond are congruent. what is the "short-hand" way of saying this?

Answer 19

the CPCTC Theorem

Answer 20

that is the reason for 5

Answer 21

Okay, thanks for your help Phi!

Answer 22

The partition postulate is used to say that the sum of 2 angles (for example) add up to a bigger angle. See the link for the exact wording.

Answer 23

Oh okay, I understand.