Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q8 (page 179)

M, N and T are the midpoints of the sides of ΔXYZ.

State how many parallelograms are in the diagram.

Short Answer

Expert verified

There are 3 parallelograms in the diagram.

Step by step solution

01

Step 1. Consider the diagram.

ΔXYZis:

Here, M, N and T are midpoints of ΔXYZ.

02

Step 2. Show the calculation.

Consider in triangles TXM and ZXY .

∠TXM=∠ZXY (Common).

TXZX=XMXY=12 (Midpoints).

Therefore, ΔTXM~ΔZXY(SAS).

∠XMT=∠XYZ∠MTX=∠YZX

Angle XMT and XYZ are the corresponding angles. Hence, line TM and ZY or ZN are parallel to each other.

Consider in triangles NMY and ZXY.

∠NYM=∠ZYX (Common).

NYZY=YMYX=12 (Midpoints).

Therefore, ΔNMY~ΔZXY(SAS).

∠YNM=∠YZX∠YMN=∠YXZ

Angle YNM and YZX are the corresponding angles. Hence, line NM and ZX or ZT are parallel to each other.

Thus, MNZT is parallelogram.

Similarly, TNXM is also a parallelogram.

Similarly, TNMY is also a parallelogram

03

Step 3. State the conclusion.

Therefore, the total number of parallelograms is 3.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Exercise 5 quad. ABCD is a parallelogram. Find the values of x, y, and z.

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free