Question

Given
Line segment NP is congruent to line segment QP
Line segment MP bisects ∠NPQ

Prove: ΔMNP ≅ ΔMQP

Select the statement with the corresponding reason for each step of the proof.

Answer 1

Line segment NP is congruent to line segment QP
∠NPM ≅ ∠QPM
Line segment MP is congruent to line segment MP
ΔMNP ≅ ΔMQQ

DEFINITIONS:
A) Given
B) Definition of Angle Bisector
C) SAS
D) Reflexive Property

Answer 2

Im thinking #1 is A
#2 is C
#3 is D
#4 is B
AM I RIGHT??

Answer 3

@phi

Answer 4

@cwrw238

Answer 5

First line
Line segment NP is congruent to line segment QP

that looks just like the first line in
Given
Line segment NP is congruent to line segment QP
Line segment MP bisects ∠NPQ

so I would say #1 is A (Given)

Answer 6

2nd line
∠NPM ≅ ∠QPM

How do we know these angles are congruent. Do they tell us in the Given?

Given
Line segment NP is congruent to line segment QP
Line segment MP bisects ∠NPQ

It does not say the angles are =. But it does say angle NPQ is bisected (divided into two equal angles)
That should tell you which of B, C or D to use.

Answer 7

i dont know i put c

Answer 8

Look at the figure. do you see angle NPQ? (put your pencil on N draw toward P, then to Q)

the Given says line MP (do you see it?) divides that angle into 2 equal parts.

Answer 9

can you name the two angles that line MP forms by dividing angle NPQ into 2 angles?

Answer 10

wait i dont see, lol am so slow

Answer 11

do you see angle NPQ? (put your pencil on N draw toward P, then to Q)

Answer 12

wait isn't number 2 angle bisector

Answer 13

yes. It would be good to notice that angle NPM and angle QPM are formed by line MP dividing the big angle NPQ into 2 angles.

Answer 14

3rd line
Line segment MP is congruent to line segment MP

this is a fancy way to say MP equals itself. There is a fancy name for saying that a thing equals itself. we used A and B, so your choices are C or D

Answer 15

that i think is reflexive which is D

Answer 16

Yes. The only way to know that is memorize reflexive property means a thing equals itself.

Answer 17

yayy and it's obvious what the last is now :D

Answer 18

4th line
ΔMNP ≅ ΔMQQ

triangles are congruent if you can show any of :
SAS side-angle-side meaning two sides and the angle between are all congruent to the other triangles 2 sides and angle
ASA angle-side-angle
SSS side-side-side show all 3 sides = the 3 sides of the other triangle.

here they showed SAS

Answer 19

yes i see now but thanks alot for your help :D

Answer 20

yw