Isosceles Triangles
ICSE · Class 9 · Mathematics
Flashcards for Isosceles Triangles — ICSE Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allSolve 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…
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°.
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°.
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…
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…
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.
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.
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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