Problems on Equal Intercepts Theorem
Here we will solve different types of problems on Equal Intercepts Theorem.
1.
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.
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. |
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.
Recent Articles
-
Circle Math | Terms Related to the Circle | Symbol of Circle O | Math
Apr 24, 24 12:50 PM
In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We… -
Fundamental Geometrical Concepts | Point | Line | Properties of Lines
Apr 24, 24 12:38 PM
The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples. -
Symmetrical Shapes | One, Two, Three, Four & Many-line Symmetry
Apr 23, 24 04:50 PM
Symmetrical shapes are discussed here in this topic. Any object or shape which can be cut in two equal halves in such a way that both the parts are exactly the same is called symmetrical. The line whi… -
Relation between Diameter Radius and Circumference |Problems |Examples
Apr 23, 24 03:15 PM
Relation between diameter radius and circumference are discussed here. Relation between Diameter and Radius: What is the relation between diameter and radius? Solution: Diameter of a circle is twice -
Preschool Math Activities | Colorful Preschool Worksheets | Lesson
Apr 21, 24 10:57 AM
Preschool math activities are designed to help the preschoolers to recognize the numbers and the beginning of counting. We believe that young children learn through play and from engaging