Mid-Point and Its Converse
ICSE · Class 9 · Mathematics
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In triangle ABC, D and E are mid-points of sides AB and AC respectively. If BC = 12 cm, what is the length of DE?
In triangle PQR, if M is the mid-point of PQ and MN is drawn parallel to QR meeting PR at N, then N divides PR in what ratio?
If P, Q, R, S are mid-points of sides AB, BC, CD, DA of quadrilateral ABCD respectively, what type of figure is PQRS?
In a trapezium ABCD where AB || CD, E is the mid-point of AD and F is the mid-point of BC. If AB = 10 cm and CD = 6 cm, find EF.
Sample Questions
Which of the following statements are true about the Mid-Point Theorem?
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DE is parallel to the third side BC, DE equals half the length of BC, The theorem applies to any triangle
The Mid-Point Theorem states that the line joining mid-points of two sides is parallel to the third side and equals half its length. This applies to all triangles.
True or False: In any triangle, the line segment joining mid-points of two sides is always perpendicular to the third side.
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False
False. The Mid-Point Theorem states that the line segment joining mid-points is parallel to the third side, not perpendicular. It's only perpendicular in special cases like right triangles.
In triangle ABC, D is mid-point of AB. If DE is drawn parallel to BC and meets AC at E, and BC = 14 cm, what is DE?
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7 cm
Since D is mid-point of AB and DE || BC, by Mid-Point Theorem, E is mid-point of AC and DE = ½BC = ½ × 14 = 7 cm.
Which conditions are necessary for the Equal Intercept Theorem?
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Three or more parallel lines, Another transversal intersecting the parallel lines
The Equal Intercept Theorem requires three or more parallel lines, one transversal making equal intercepts, and another transversal which will also make equal intercepts.
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