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Isosceles Triangles — Flashcards

ICSE · Class 9 · Mathematics

20 flashcards for Isosceles Triangles (ICSE Class 9 Mathematics) to test yourself on key terms and facts. Part of the ICSE Class 9 Mathematics syllabus.

35 questions20 flashcards8 formulas & key relations5 concepts

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A labeled diagram illustrating an isosceles triangle with two equal sides and the angles opposite to them also being equal. Includes the definition of an equilateral triangle as a special case.
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20 Flashcards·
Base angles theoremAngle sum in isosceles triangleTheorem 1 applicationProof strategyConverse of base angles theoremRelationship between triangle types
Card 1Base angles theorem

Solve the problem: In triangle ABC, AB = AC. Find the relationship between angle B and angle C.

Answer

Step 1: AB = AC means the two sides opposite angle B and angle C are equal. Step 2: In an isosceles triangle, angles opposite equal sides are equal. Step 3: Therefore, angle B = angle C. Answer: angle…

Card 2Base angles theorem

Apply the base angles theorem: In triangle ABC, AB = AC and angle B = 55°. Find angle C.

Answer

Step 1: AB = AC, so the angles opposite them are equal. Step 2: Angle B = angle C. Step 3: Since angle B = 55°, angle C = 55°. Answer: angle C = 55°.

Card 3Angle sum in isosceles triangle

Solve: In triangle ABC, AB = AC and angle B = angle C = 70°. Find angle A.

Answer

Step 1: Sum of angles in a triangle = 180°. Step 2: angle A + 70° + 70° = 180°. Step 3: angle A + 140° = 180°. Step 4: angle A = 180° - 140° = 40°. Answer: angle A = 40°.

Card 4Theorem 1 application

When do you use the statement: If two sides of a triangle are equal, the angles opposite to them are also equal?

Answer

Use it when two sides of a triangle are given equal and the required result is an angle relation. Worked example: If AB = AC in triangle ABC, then angle B = angle C. This helps find missing angles qui…

Card 5Proof strategy

Solve the proof idea: Why is AD drawn perpendicular to BC in the proof of the base angles theorem?

Answer

Step 1: Draw AD perpendicular to BC. Step 2: Then angle ADB = angle ADC = 90°. Step 3: In triangles ABD and ACD, AB = AC, AD = AD, and right angles are equal. Step 4: The two triangles become congruen…

Card 6Converse of base angles theorem

Solve the converse problem: In triangle ABC, angle B = angle C. Prove that AB = AC.

Answer

Step 1: Draw AD perpendicular to BC. Step 2: In triangles ABD and ACD, angle B = angle C. Step 3: angle ADB = angle ADC = 90°. Step 4: AD = AD is common. Step 5: The triangles are congruent by A.A.S.

Card 7Converse of base angles theorem

Apply the converse theorem: In triangle ABC, angle B = angle C = 48°. What can be said about AB and AC?

Answer

Step 1: Equal angles in a triangle have opposite equal sides. Step 2: Angle B = angle C. Step 3: Therefore, AB = AC. Answer: AB = AC.

Card 8Relationship between triangle types

Why does an equilateral triangle satisfy isosceles-triangle properties?

Answer

Step 1: In an equilateral triangle, all three sides are equal. Step 2: That means at least two sides are equal. Step 3: So it fits the isosceles-triangle condition. Step 4: Therefore, all isosceles-tr…

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Frequently Asked Questions

What are the important topics in Isosceles Triangles for ICSE Class 9 Mathematics?
Key topics in Isosceles Triangles include Core ideas and definitions, Important theorem proofs, Other properties of isosceles triangles, Solved problem patterns to remember. Study these first, then practise questions on each for Class 9 exams.
How many flashcards are available for Isosceles Triangles?
There are 20 flashcards for Isosceles Triangles covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Isosceles Triangles for Class 9 exams?
Learn the core ideas first, then work through the 35 practice questions on Isosceles Triangles. 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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