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.
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Explore the full setSolve: In triangle ABC, D and E are the mid-points of AB and AC. What can be concluded about DE?
Answer
Step 1: Use the Mid-Point Theorem. Step 2: The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it. Step 3: Therefore, DE // BC and DE = 1/2 BC…
Apply the Mid-Point Theorem: In triangle ABC, D and E are mid-points of AB and AC. If BC = 14 cm, find DE.
Answer
Step 1: Use DE = 1/2 BC. Step 2: Substitute BC = 14 cm. Step 3: DE = 1/2 × 14 = 7 cm. Answer: DE = 7 cm.
Solve: In triangle ABC, D and E are the mid-points of AB and AC. If DE = 6 cm, find BC.
Answer
Step 1: Use DE = 1/2 BC. Step 2: Substitute DE = 6 cm. Step 3: 6 = 1/2 BC. Step 4: Multiply both sides by 2. BC = 12 cm. Answer: BC = 12 cm.
Why does the segment joining the mid-points of two sides of a triangle become parallel to the third side?
Answer
The idea comes from congruent triangles formed after drawing a suitable parallel line. The equal halves on two sides create matching angles and lengths, so the small triangle and the larger triangle f…
State the Mid-Point Theorem in a usable formula form.
Answer
Formula: DE // BC and DE = 1/2 BC, where D and E are the mid-points of AB and AC in triangle ABC. Quick example: if BC = 10 cm, then DE = 5 cm.
Solve: In triangle ABC, D is the mid-point of AB and DE is drawn parallel to BC. What can be said about E on AC?
Answer
Step 1: Use the Converse of the Mid-Point Theorem. Step 2: A line through the mid-point of one side of a triangle, parallel to another side, bisects the third side. Step 3: So E is the mid-point of AC…
Solve: In triangle ABC, D is the mid-point of AB and DE is parallel to BC. If AC = 18 cm, find AE and EC.
Answer
Step 1: Since DE // BC and D is the mid-point of AB, E is the mid-point of AC. Step 2: So AE = EC. Step 3: AC = AE + EC = 18 cm. Step 4: AE = EC = 18/2 = 9 cm. Answer: AE = 9 cm and EC = 9 cm.
Why does a line through the mid-point of one side of a triangle and parallel to another side bisect the third side?
Answer
This works because the parallel line creates equal corresponding angles, and the triangle formed matches the original shape in a way that forces equal division on the third side. So the parallel segme…
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