Geometry

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By Basic Proportionality Theorem (Thales Theorem): AD/DB = AE/EC Step 1: Write the proportion → 4/6 = 5/EC Step 2: Cross multiply → 4 × EC = 6 × 5 Step 3: 4 × EC = 30 Step 4: EC = 30/4 = 7.5 cm Verifi…

Answer

Check if corresponding sides are proportional using SSS similarity criterion. Step 1: Find ratios of corresponding sides → AB/PQ = 6/9 = 2/3 → BC/QR = 8/12 = 2/3 → AC/PR = 10/15 = 2/3 Step 2: Check if…

Answer

Use similar triangles: △ABE ~ △CDE where E is the tip of shadow. Let shadow length = x Step 1: Set up proportion from similar triangles → Height of lamp/Shadow from lamp = Height of boy/Shadow of boy …

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Use AA similarity when: - You know two pairs of corresponding angles are equal - The third angle will automatically be equal (since angle sum = 180°) - You cannot or don't need to know side lengths E…

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Given: AD/DB = 3/4 and AE/EC = 3/4 Step 1: Identify what you're given → AD/DB = AE/EC (both equal 3/4) Step 2: Apply Converse of BPT → If a line divides two sides of a triangle in the same ratio, th…

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Use Angle Bisector Theorem: AB/AC = BD/DC Given: AB = 8 cm, AC = 12 cm, BC = 10 cm Let BD = x, then DC = 10 - x Step 1: Apply Angle Bisector Theorem → 8/12 = x/(10-x) Step 2: Simplify the left side…

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Use Pythagoras Theorem: a² + b² = c² where c is hypotenuse Given: Hypotenuse c = 13 cm, One leg a = 5 cm, Find b = ? Step 1: Write Pythagoras formula → a² + b² = c² Step 2: Substitute known values …

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Use Pythagoras Theorem: a² + b² = c² Given: Ladder length (hypotenuse) c = 5 m, Distance from wall a = 3 m, Height b = ? Step 1: Identify the right triangle → Ladder is hypotenuse → Distance from wa…