Triangles
Karnataka Board · Class 10 · Mathematics
Flashcards for Triangles — Karnataka Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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In triangle ABC, DE is parallel to BC. If AD = 3 cm, DB = 6 cm, and AE = 4 cm, find EC.
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…
Prove that all circles are similar. Explain why with an example.
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…
In triangle PQR, ST is drawn parallel to QR. If PS/SQ = 2/3 and PT/TR = 2/3, verify that ST || QR using the converse of Basic Proportionality Theorem.
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…
When do you use the AA similarity criterion? Solve: Triangle ABC has angles 60° and 80°. Triangle DEF has angles 60° and 40°. Are they similar?
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…
Apply SSS similarity criterion: Triangle ABC has sides 6 cm, 8 cm, 10 cm. Triangle PQR has sides 9 cm, 12 cm, 15 cm. Are they similar?
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 = …
A 1.5 m tall person casts a 2 m shadow. At the same time, a building casts a 40 m shadow. Find the height of the building using similar triangles.
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/…
Use SAS similarity criterion: Triangle ABC has AB = 4 cm, AC = 6 cm, ∠A = 70°. Triangle DEF has DE = 6 cm, DF = 9 cm, ∠D = 70°. Prove similarity.
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…
In trapezium ABCD with AB || CD, diagonals intersect at O. If AO = 6 cm, OC = 9 cm, find BO/OD ratio.
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…
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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