Similar Triangles — Flashcards
Telangana Board · Class 10 · Mathematics
30 flashcards for Similar Triangles (Telangana Board Class 10 Mathematics) to test yourself on key terms and facts.
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Solve using the mirror method idea: In a similar-triangles setup, if DE || BC and AD/DB = 3/5, AC = 5.6 cm, find AE.
Answer
Use Basic Proportionality Theorem: AD/DB = AE/EC = 3/5. So AE:EC = 3:5. Let AE = 3x and EC = 5x. Then AC = AE + EC = 8x = 5.6 cm. So x = 0.7 cm. AE = 3x = 2.1 cm. Answer: AE = 2.1 cm.
Apply BPT: In a triangle, LM || AB. If AL = x - 3, AC = 2x, BM = x - 2, BC = 2x + 3, find x.
Answer
Since LM || AB, corresponding sides are divided in the same ratio. So AL/LC = BM/MC. LC = AC - AL = 2x - (x - 3) = x + 3. MC = BC - BM = (2x + 3) - (x - 2) = x + 5. Now (x - 3)/(x + 3) = (x - 2)/(x + …
Use the converse of BPT: If AD/DB = AE/EC, what can be concluded about DE and BC?
Answer
If a line divides two sides of a triangle in the same ratio, then it is parallel to the third side. So DE || BC. Quick check: this is the converse of BPT, not the direct theorem.
Why are the triangles in the tree-and-mirror method similar and not congruent?
Answer
They have the same shape, so they are similar. Their sizes are different, so they are not congruent. A scale factor relates their corresponding sides. If the scale factor is K: K > 1 gives enlarged fi…
Formula for the scale factor in similar triangles.
Answer
Scale factor K = DE/AB = EC/BC = DC/AC. Here, DE, EC, DC correspond to AB, BC, AC. Quick example: if DE = 6 cm and AB = 3 cm, then K = 6/3 = 2. That means the new triangle is enlarged by a factor of 2…
If two triangles have equal corresponding angles, what can be said about their sides and similarity?
Answer
Equal corresponding angles imply proportional corresponding sides. So the triangles are similar. This is the AAA similarity criterion, also called AA similarity because the third angle is automatic. R…
Solve by AAA similarity: If triangle ABC is similar to triangle DEF and AB = 3 cm, DE = 4.5 cm, BC = 6 cm, find EF.
Answer
For similar triangles, corresponding sides are proportional. AB/DE = BC/EF. Substitute values: 3/4.5 = 6/EF. Cross-multiply: 3EF = 4.5 × 6 3EF = 27 EF = 9 cm. Answer: EF = 9 cm.
When do you use SSS similarity?
Answer
Use SSS similarity when all three pairs of corresponding sides are proportional. Then the triangles are similar, and their corresponding angles are equal. Example: If AB/DE = BC/EF = AC/DF, then trian…
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