Question

In ΔPQR shown below, segment QS is an altitude:
What property or definition is needed to prove that ΔPSQ is similar to ΔQSR?

Answer 1

Transitive Property of Equality

Reflexive Property of Equality

Definition of an Altitude

Definition of Supplementary Angles

Answer 2

http://learn.flvs.net/webdav/assessment_images/educator_geometry/v15/module05/05_10_b19.jpg

Answer 3

like that?

Answer 4

yes

Answer 5

ok i think its reflexive property of equality because angle QSR is congruent to angle QSP because they are both 90 degrees. QS bisects angle PQR so angles SQR and PQS are congruent. therefore;
angle QSR equals angle QSP
angle PQS equals RQS
so angle QRS must equal angle QPS

all angles are equal so the triangles must be similar

Answer 6

see how this is the reflexive property?

Answer 7

because it shows how angles are equal

Answer 8

Also just by the definition of an altitude

Answer 9

i think the best answer is the definition of an altitude but the second choice is also good

Answer 10

yes i saw that but can you please explain how this makes the angles equal

Answer 11

i did look at my first post

Answer 12

read carefully what i wrote

Answer 13

basically you can prove that the angles in both the triangles are equal so they are similar

Answer 14

an altitude always splits an angle in 1/2

Answer 15

now do you get what i wrote?

Answer 16

yes thank you so much

Answer 17

ok hope i helped

Answer 18

you don't know what a life saver you are :)

Answer 19

remember it can be definition of altitude or reflexive property

Answer 20

i think if you choose one just tell your teacher how you proved it

Answer 21

yes i will

Answer 22

my teacher is very understanding

Answer 23

Reflexive Property of Equality, is incorrect.

Answer 24

@swifty what was the answer