Similarity Of Triangles
NIOS · Class 10 · Maths
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Solve: In triangle ABC, if DE is parallel to BC, AD = 3 cm, DB = 5 cm, and AE = 6 cm, find AC.
Answer
Step 1: Use Basic Proportionality Theorem: (AD)/(DB) = (AE)/(EC). Step 2: Substitute values: 3/5 = 6/EC. Step 3: Cross-multiply: 3 × EC = 5 × 6 = 30. Step 4: EC = 10 cm. Step 5: AC = AE + EC = 6 + 10 …
When do you use the Basic Proportionality Theorem? Apply it to a triangle with a line parallel to one side.
Answer
Use it when a line is drawn parallel to one side of a triangle and intersects the other two sides. Formula: (AD)/(DB) = (AE)/(EC) Meaning: AD and DB are the two parts of one side, and AE and EC are th…
Is DE parallel to BC? Given AD = 4 cm, DB = 5 cm, AE = 4.5 cm, and EC = 5 5/8 cm.
Answer
Step 1: Check the ratio AD/DB = 4/5. Step 2: Convert EC = 5 5/8 = 45/8 cm. Step 3: Check AE/EC = 4.5/(45/8) = 4.5 × 8 / 45 = 4/5. Step 4: The ratios are equal. Answer: DE is parallel to BC by the conv…
Find x: In triangle ABC, AD = 4.5 cm, AB = 6 cm, AC = 8 cm, and AD is the bisector of angle A. Find CD.
Answer
Step 1: Use Angle Bisector Theorem: (BD)/(DC) = (AB)/(AC). Step 2: Substitute values: 4.5/x = 6/8. Step 3: Cross-multiply: 6x = 4.5 × 8. Step 4: 6x = 36. Step 5: x = 6 cm. Answer: CD = 6 cm.
Solve: A triangle has sides 28 cm, 36 cm, and 48 cm. The bisector of the angle opposite the smallest side meets that side at D. Find BD and DC.
Answer
Step 1: The smallest side is 28 cm, so the opposite angle is bisected. Step 2: Use Angle Bisector Theorem: BD/DC = AB/AC = 36/48 = 3/4. Step 3: Let BD = 3k and DC = 4k. Step 4: BD + DC = 28, so 3k + 4…
Why are a rectangle and a square not similar?
Answer
Two polygons are similar only if corresponding angles are equal and corresponding sides are proportional. A rectangle and a square have equal corresponding angles, but their sides are not proportional…
Which pairs are similar and which are congruent? 1) Two line segments of the same length 2) Two line segments of different lengths 3) Two circles of the same radius 4) Two circles of different radii
Answer
Step 1: Same length line segments are congruent and similar. Step 2: Different length line segments are similar but not congruent. Step 3: Circles with the same radius are congruent and similar. Step …
What does the symbol ~ mean in similarity of triangles?
Answer
The symbol ~ means 'is similar to'. Example: If triangle ABC ~ triangle DEF, then corresponding angles are equal and corresponding sides are proportional. Quick check: If AB/DE = BC/EF = CA/FD, then t…
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