Question

Use ΔDEF shown below to answer the question that follows:

http://prntscr.com/96mdpg

Which of the following must be given to prove that ΔDEF is similar to ΔGDF?

Segment DG is an altitude of ΔDEF.
Segment EF is a hypotenuse.
Segment ED is shorter than segment DF.
Angle E is congruent to itself.

Is it either B or D? I'm honestly not sure

Answer 1

@TheSmartOne

Answer 2

@jim_thompson5910

Answer 3

`Segment EF is a hypotenuse.`
that's already given and not useful in this case

notice how angle FDE = 90 degrees (because of the square angle marker)
the side opposite that is the hypotenuse, which is the longest side

Answer 4

`ΔDEF is similar to ΔGDF`

D shows up twice
F shows up twice

angle D changes between these two triangles
angle F stays the same. This is known as the overlapping angle (or shared angle or common angle)

Answer 5

wait, so what does that tell us? I don't get it.

Answer 6

`B) Segment EF is a hypotenuse.` is true but it's not relevant. So choice B is out

Answer 7

`Angle E is congruent to itself.` is true by the reflexive property but again, not relevant

E would have to show up twice for it to be useful

Answer 8

Oh, okay.

Answer 9

`Segment ED is shorter than segment DF.`

too vague and not quantitative enough, so this is out too

Answer 10

So A is all that's left.. but what does the word 'altitude' mean in there?

Answer 11

`Segment DG is an altitude of ΔDEF.` this is true and useful

if we know DG is an altitude then angle DGF = 90 degrees

this will pair up with angle FDE = 90 degrees

these two angles form one pair of the AA similarity angle theorem

Answer 12

the other pair would be F and itself

Answer 13

Okay... I guess that answer just didn't make much sense to me because I've seen the word 'altitude' used in a mathematical sense.

Answer 14

*I've never seen

Answer 15

in terms of geometry and triangles, it is the line segment drawn from one vertex to the opposite side such that it is perpendicular to the segment

http://www.gogeometry.com/problem/p029_triangle_altitude.gif

Answer 16

Oh, if I would've looked that up, that answer would've been right from the beginning lol

Thanks!

Answer 17

no problem