Question

Paul walks 25 feet away from his house and places a mirror on the ground. He backs 5 feet away from the mirror so that he can see the tip of the roof. Paul's eyes are 6 feet above the ground. The angles between the top of the house, the mirror, and the ground and between Paul's eyes, the mirror, and the ground are congruent as shown in the image:

Image depicts a mirror on the ground between a person and a house. The mirror is 4 feet away from the person and 15 feet away from the house.

Part 1: Prove the triangles are similar.
Part 2: Determine the height of the house.

Answer 1

@Preetha

Answer 2

@primeralph @agent0smith @SolomonZelman

Answer 3

WILL GIVE METAL!!

Answer 4

Two triangles are similar because of AA...If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. The house with the ground is 90 degrees and the person with the ground is 90 degrees..thats one pair of equal angles. And the other given pair. So we have two pairs of angles equal to each other, hence, the triangles are similar.

Answer 5

To determine the height of the house, set up a proportion.

When two triangles are similar, the corresponding sides are in proportion.

Answer 6

6/height of house = 5/25

or 6/h = 5/25

Cross-multiply, you get 5h = 150

h = 30

The height of the house is 30 feet.

Answer 7

So the base of the bigger triangle is 25 and the base of the smaller is 5, then the hypotenuse of the smaller is 6. So would i do 25/5 = x/6 or the other way around? And thanks fo much for the first

Answer 8

Oh , let me read yours

Answer 9

Done.

Answer 10

Yah so 30 feet!

Answer 11

Yes!

Answer 12

Thanks so much!! How do i give you a medal? :P

Answer 13

Just a "thanks" is sufficient.

Answer 14

Ok, thanks ! :D

Answer 15

If you have any spare time @Easyaspi314 heres a question i already did, if you could make sure im right that would be great. Thanks again!


Prove the Converse of the Pythagorean Theorem using similar triangles. The Converse of the Pythagorean Theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures.


My answer


So we have one triangle labeled ACB and with b in the middle of AC and a in the middle of BC and c in the middle of AB. Then we construct another triangle DFE with b in the middle of DF and a in the middle of FE.

If a2+b2=c2 then DABC is a right angled triangle with right angle at C.

Proof

1. EF=BC=a AND FD=CA=b- Because DF is a right angle

2. EF=NC=a - Angle F is a right triangle

3. FD=CA=b = Because of the puthagoras theorem the given AB=c= square root of a2+b2 t

4. AB=DE
BC=EF
CA=FD - By construction

5. Triangle ABC is congurent to triangle DEF by SSS Side Side Side

Answer 16

That would be one approach.

Answer 17

Ok, cool. What the other way be? Using another theorem?

Answer 18

There are so many ways. It could be shown the triangles are congruent by SAS.

Answer 19

Ah, ok! thanks so much for the help.