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Mathematics 51 Online
OpenStudy (krissysivan):

The figure below shows segments PQ and RS which intersect at point T. Segment PR is parallel to segment SQ. Two line segments PQ and RS intersect at T. Segments PR and SQ are parallel to each other. Which of these facts is used to prove that triangle PTR is similar to triangle QTS? Line segment RT is congruent to line segment TP. Line segment ST is congruent to line segment TQ. Angle PTR is congruent to angle QTS. Angle PRT is congruent to angle QTS.

OpenStudy (krissysivan):

OpenStudy (krissysivan):

@duckerstar146

OpenStudy (duckerstar146):

Just based on the picture given, we can cross off the first two answer choices, as those deal with lines, and not angles

OpenStudy (duckerstar146):

My answer would be C, due to the order of the angles. In D, they aren't the same but in C, they are if that makes sense to you.

OpenStudy (krissysivan):

Its sounds right to me

OpenStudy (duckerstar146):

Well me too!

OpenStudy (krissysivan):

Look at the figure below: Triangles ABE and BDE have a common side BE. C is the point of intersection of BD and AE. AC equals EC and CD equals CB. Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? Triangle ABE and triangle BEC Triangle ABC and triangle EBC Triangle BCE and triangle DCE Triangle ACB and triangle ECD

OpenStudy (krissysivan):

OpenStudy (duckerstar146):

My answer for this would be D, because as said before, look at what is a line and what is an angle

OpenStudy (duckerstar146):

And, also look for the correct order

OpenStudy (krissysivan):

ok, thank you

OpenStudy (duckerstar146):

No Problem

OpenStudy (krissysivan):

i have 4 more questions

OpenStudy (duckerstar146):

Seems good to me

OpenStudy (krissysivan):

The figure below shows two triangles EFG and KLM: Two triangles EFG and KLM are drawn. Angle KML is a right angle. The measures of the sides of the triangles are, In triangle EFG, EG measures a, GF measure b, and EF measures c. In triangle KLM, KM measures a and ML measures b. Which of the following can be used to prove that triangle EFG is also a right triangle? Use Pythagorean Theorem to prove that KL is equal to c. Prove that the ratio of EF and KL is greater than 1 and hence, the triangles are similar by AA postulate. Prove that the sum of the squares of a and c is greater than square of b. Prove that the sum of the squares of a and b is greater than square of c.

OpenStudy (krissysivan):

OpenStudy (duckerstar146):

A, because they are a group of two similar triangles

OpenStudy (duckerstar146):

Since they share the same variables, we can assume they are the same.

OpenStudy (duckerstar146):

Between triangles

OpenStudy (krissysivan):

This one? Use Pythagorean Theorem to prove that KL is equal to c.

OpenStudy (duckerstar146):

Yup

OpenStudy (krissysivan):

Look at the figure shown below: A triangle RPQ is shown. S is a point on side PQ and T is a point on side PR. Points S and T are joined using a straight line. The length of PS is equal to 28, the length of SQ is equal to 2x, the length of PT is equal to 35 and the length of TR is equal to 60. Rita is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 24. Statement Reason 1. Segment ST is parallel to segment QR Given 2. Angle QRT is congruent to angle STP Corresponding angles formed by parallel lines and their transversal are congruent 3. Angle SPT is congruent to angle QPR Reflexive property of angles 4. Triangle SPT is similar to triangle QPR Angle-Angle Similarity Postulate 5. (2x + 28):95 = Corresponding sides of similar triangles are in proportion Which of the following can she use to complete statement 5? 28:95 28:35 60:95 60:35

OpenStudy (krissysivan):

OpenStudy (duckerstar146):

so PQ = 2x+28 similarly, PR = 95 since PT = 35 TR = 60 PT+TR = 35+60 = 95 = PR

OpenStudy (duckerstar146):

So look at the numbers of the left side of the triangles, and then the right side of the triangles, and you should see; (2x + 28) : 95 Meaning that the ratio of that is PQ: PR

OpenStudy (krissysivan):

would it be A? 28:95

OpenStudy (krissysivan):

or 60:95?

OpenStudy (duckerstar146):

However, there is another ratio, PQ: PR = PS: PT (2x + 28) : 95 = 28: 35 Make Sense?

OpenStudy (krissysivan):

kind of. So its A?

OpenStudy (duckerstar146):

Look at the answers again, and which one matches 28:35

OpenStudy (krissysivan):

ooppss, B, LOL

OpenStudy (duckerstar146):

There you go!

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