Problems on Equal Intercepts Theorem

Here we will solve different types of problems on Equal Intercepts Theorem.

1. 

Problems on Equal Intercepts Theorem

In the above figure, MN ∥ KL ∥ GH and PQ = QR. If ST = 2.2 cm, find SU.

Solution:

The transversal PR makes equal intercepts, PQ and QR, on the three parallel lines MN, KL and GH.

Therefore, by the Equal Intercepts Theorem, ST = TU = 2.2 cm.

Therefore, SU = ST + TU = 2.2 cm + 2.2 cm = 4.4 cm.


2. In a quadrilateral JKLM, JK ∥ LM. A line parallel to LM is drawn through the midpoint X of KL, which meets JM at Y. Prove that XY bisects JM.

Solution:

Given: In the quadrilateral JKLM, JK ∥ LM. X is the midpoint of KL and XY ∥ LM.

Problems on Equal Intercepts

To prove: XY bisects JM.

Proof:

          Statement

          Reason

1. JK ∥ LM ∥ XY.

1. JK ∥ LM and XY ∥ LM.

2. KL makes equal intercepts on JK, XY and LM.

2. Given that KX = XL.

3. JM also makes equal intercepts on JK, XY and LM.

3. By the Equal Intercepts Theorem.

4. JY = YM.

5. From statement 3.

5. XY bisects JM. (Proved).

5. From statement 4.






9th Grade Math

From Problems on Equal Intercepts Theorem to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

RSS

  1. Worksheet on Yesterday, Today and Tomorrow | Sequence of the Week-days

    Nov 25, 24 01:18 AM

    Practice the worksheet on yesterday, today and tomorrow, the questions are based on the sequence of the week-days, their names and order. We know, the present day is today, the day before today

    Read More

  2. Yesterday, Today and Tomorrow | Name of each Day of the Week

    Nov 25, 24 01:09 AM

    We will learn the relation between yesterday, today and tomorrow. There are seven days in a week. We know the name of each day of the week. Sunday is known as the first day of the week.

    Read More

  3. The Story about Seasons | Spring | Summer | Autumn | Winter

    Nov 25, 24 12:48 AM

    The Four Seasons
    Kids let’s enjoy the story about seasons. Here we will discuss about the four seasons and the duration. Some months are too hot and some are too cold. The period of hot months is called the hot

    Read More

  4. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Nov 25, 24 12:17 AM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  5. Time Duration |How to Calculate the Time Duration (in Hours & Minutes)

    Nov 24, 24 11:01 PM

    Time Duration Example
    Time duration tells us how long it takes for an activity to complete. We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton…

    Read More