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Mid-Point and Its Converse — Flashcards

ICSE · Class 9 · Mathematics

25 flashcards for Mid-Point and Its Converse (ICSE Class 9 Mathematics) to test yourself on key terms and facts.

34 questions25 flashcards5 formulas & key relations5 concepts

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A step-by-step visual proof of the Mid-Point Theorem, showing a triangle ABC with D and E as mid-points of AB and AC respectively. Construction involves drawing CF parallel to BA, extending DE to F, a
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25 Flashcards·
Mid-Point TheoremConverse of Mid-Point Theorem
Card 1Mid-Point Theorem

Solve: 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…

Card 2Mid-Point Theorem

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.

Card 3Mid-Point Theorem

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.

Card 4Mid-Point Theorem

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…

Card 5Mid-Point Theorem

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.

Card 6Converse of Mid-Point Theorem

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…

Card 7Converse of Mid-Point Theorem

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.

Card 8Converse of Mid-Point Theorem

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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Frequently Asked Questions

What are the important topics in Mid-Point and Its Converse for ICSE Class 9 Mathematics?
Key topics in Mid-Point and Its Converse include Mid-Point Theorem, Converse of Mid-Point Theorem, Applications of the Mid-Point Theorem, Equal Intercept Theorem and Its Use. Study these first, then practise questions on each for Class 9 exams.
How many flashcards are available for Mid-Point and Its Converse?
There are 25 flashcards for Mid-Point and Its Converse covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Mid-Point and Its Converse for Class 9 exams?
Learn the core ideas first, then work through the 34 practice questions on Mid-Point and Its Converse. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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