Triangles

Answer

Step 1: Apply Basic Proportionality Theorem - When DE || BC, then AD/DB = AE/EC Step 2: Substitute values → 3/6 = 4/EC Step 3: Cross multiply → 3 × EC = 6 × 4 = 24 Step 4: Solve for EC → EC = 24/3 = 8

Answer

Step 1: Definition of similarity - Two figures are similar if they have same shape but not necessarily same size Step 2: All circles have the same shape (perfectly round) regardless of their radius St

Answer

Step 1: Given PS/SQ = 2/3 and PT/TR = 2/3 Step 2: Check if the ratios are equal → PS/SQ = PT/TR = 2/3 ✓ Step 3: Apply Converse of Basic Proportionality Theorem: If a line divides two sides of a triang

Answer

Use AA criterion when: Two angles of one triangle equal two angles of another triangle Step 1: Find third angle of ABC → 180° - 60° - 80° = 40° Step 2: Angles of ABC: 60°, 80°, 40° Step 3: Angles of D

Answer

Step 1: Check if corresponding sides are proportional Step 2: Arrange sides in order: ABC (6, 8, 10) and PQR (9, 12, 15) Step 3: Calculate ratios: AB/PQ = 6/9 = 2/3 BC/QR = 8/12 = 2/3 CA/RP = 10/15 =

Answer

Step 1: Set up similar triangles - person and shadow form one triangle, building and shadow form another Step 2: Both triangles are similar (same sun angle) Step 3: Write proportion: Height of person/

Answer

Step 1: Check if one angle is equal and including sides are proportional Step 2: Given angles: ∠A = ∠D = 70° ✓ Step 3: Check including sides ratio: AB/DE = 4/6 = 2/3 AC/DF = 6/9 = 2/3 Step 4: Includin

Answer

Step 1: In trapezium with parallel sides, diagonals create similar triangles Step 2: Triangles AOB and COD are similar (AB || CD creates equal corresponding angles) Step 3: For similar triangles: AO/O