Midpoint Theorem (Motivate) MCQs Quiz | Class 9
This quiz covers Unit IV: Geometry, specifically the Midpoint Theorem for Class IX Mathematics (Code 041). The questions focus on the concept that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half of its length. Test your understanding, view the correct answers, and download the PDF solution sheet for offline revision.
Understanding the Midpoint Theorem
The Midpoint Theorem is a fundamental concept in Euclidean geometry, particularly within Class 9 Mathematics (Unit IV). It establishes a critical relationship between the midpoints of two sides of a triangle and the third side. This theorem is essential for solving complex problems involving triangles and quadrilaterals.
Statement of the Theorem
The Midpoint Theorem: The line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half of it.
The Converse: The line drawn through the midpoint of one side of a triangle, parallel to another side, bisects the third side.
Key Properties & Applications
- Parallelism: If D and E are midpoints of sides AB and AC in Triangle ABC, then DE is parallel to BC.
- Length Relationship: The length of DE is exactly half the length of BC (DE = 0.5 * BC).
- Area Relationship: The triangle formed by joining the midpoints of the three sides of a triangle divides the original triangle into four congruent triangles. The area of the inner triangle is 1/4th of the original triangle.
- Quadrilaterals: The quadrilateral formed by joining the midpoints of the sides of any quadrilateral, in order, is a parallelogram.
Quick Revision Summary
| Scenario | Conclusion |
|---|---|
| Line joins midpoints of 2 sides | Parallel to 3rd side & Half of 3rd side |
| Line from midpoint parallel to 2nd side | Bisects the 3rd side (Converse) |
| Triangle formed by 3 midpoints | Original Triangle Area / 4 |
Extra Practice Questions
1. In Triangle XYZ, M and N are midpoints of XY and XZ. If MN = 6 cm, find YZ.
2. In Triangle ABC, D is the midpoint of AB. A line parallel to BC intersects AC at E. If AC = 14 cm, find AE.
3. Prove that the figure formed by joining the midpoints of a rectangle is a rhombus.
4. If the perimeter of Triangle ABC is 40 cm, what is the perimeter of the triangle formed by joining its midpoints?
5. In an equilateral triangle of side 10 cm, what is the length of the line segment joining the midpoints of any two sides?
Content created and reviewed by the CBSE Quiz Editorial Team based on the latest NCERT textbooks and CBSE syllabus. Our goal is to help students practice concepts clearly, confidently, and exam-ready through well-structured MCQs and revision content.