Mid-Point and Its Converse
ICSE · Class 9 · Mathematics
Flashcards for Mid-Point and Its Converse — ICSE Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
What is the Mid-Point Theorem?
Answer
The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it. If D and E are mid-points of sides AB and AC of triangle ABC, then DE ∥
State the Converse of the Mid-Point Theorem.
Answer
The straight line drawn through the mid-point of one side of a triangle and parallel to another side bisects the third side. If D is mid-point of AB and DE ∥ BC, then E is the mid-point of AC.
In triangle ABC, if P and Q are mid-points of AB and AC respectively, and BC = 12 cm, find PQ.
Answer
By Mid-Point Theorem, PQ = ½BC = ½ × 12 = 6 cm. The line segment joining mid-points is always half the length of the third side.
What happens when you join the mid-points of adjacent sides of any quadrilateral?
Answer
The figure formed by joining the mid-points of adjacent sides of any quadrilateral is always a parallelogram. This is proven using the Mid-Point Theorem applied to the diagonals of the original quadri
What is the Equal Intercept Theorem?
Answer
If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts. This means if PQ = QR on parallel lines, then any other trans
In triangle ABC, D is mid-point of AB and DE ∥ BC. If AC = 8 cm, find AE.
Answer
By Converse of Mid-Point Theorem, E is the mid-point of AC. Therefore, AE = ½AC = ½ × 8 = 4 cm. When a line through mid-point is parallel to third side, it bisects the remaining side.
What special property does the line segment joining mid-points of non-parallel sides of a trapezium have?
Answer
In a trapezium, the line segment joining the mid-points of non-parallel sides is parallel to the parallel sides and its length equals half the sum of the parallel sides. If AB ∥ DC and EF joins mid-po
How do you prove that a figure formed by joining mid-points is a parallelogram?
Answer
Use the Mid-Point Theorem on triangles formed by diagonals. Show that opposite sides are parallel and equal by proving they are both parallel to the same diagonal and equal to half of it. This makes o
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