Question

The figure shows three right triangles. Triangles PQS, QRS, and PRQ are similar.

Theorem: If two triangles are similar, the corresponding sides are in proportion.



Using the given theorem, which two statements help to prove that if segment PR is x, then x2 = 97?

Segment PR × segment PS = 16
Segment PR × segment SR = 36

Segment PR × segment PS = 36
Segment PR × segment SR = 81

Segment PR × segment PS = 16
Segment PR × segment SR = 81

Segment PR × segment PS = 81
Segment PR × segment SR = 16

Answer 1

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1000_Subtest_02_10/image0034e8c7ce9.jpg

Answer 2

I figured out that PR=9.84

Answer 3

How did you figure that out?

Answer 4

I used the Pythagorean Theorem. \[4^{2}+9^{2}=c ^{2}\]

Answer 5

16+81=97
\[\sqrt{97}\approx9.85\]
My bad it's 9.85

Answer 6

Okay, you're half way through! Did you take that the altitude to the hypotenuse of a right triangle separates the hypotenuse into two segments such that the length of each leg of the triangle is the geometric mean of the lengths of the hypotenuse and the segments adjacent to that? Or does it sound confusing? :P

Answer 7

I'm confused...

Answer 8

Okay for get all that then^ :)

Answer 9

Do you think you can help on this one instead?

The figure below shows a parallelogram ABCD. Side AB is parallel to side DC and side AD is parallel to side BC.



A student wrote the following sentences to prove that parallelogram ABCD has two pairs of opposite sides equal.
For triangles ABD and CDB alternate interior angle ABD is congruent to angle CDB because AB and DC are parallel lines. Similarly, alternate interior angle ADB is equal to angle CBD because AD and BC are parallel lines. DB is equal to DB by reflexive property. Therefore, triangles ABD and CDB are congruent by SAS postulate. Therefore, AB is congruent to DC and AD is congruent to BC by CPCTC.
Which statement best describes a flaw in the student’s proof?

Angle ADB is congruent to angle CBD because they are vertical angles.

Angle ADB is congruent to angle CBD because they are corresponding angles.

Triangles ABD and CDB are congruent by SSS postulate.

Triangles ABD and CDB are congruent by ASA postulate.

Answer 10

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1000_Subtest_04_17/image0034e8c7278.jpg