Similarity — Flashcards
Maharashtra Board · Class 10 · Mathematics
30 flashcards for Similarity (Maharashtra Board Class 10 Mathematics) to test yourself on key terms and facts.
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Solve: In triangle ABC, line PQ is parallel to BC, P lies on AB and Q lies on AC. Find the relationship between AP, PB, AQ, and QC.
Answer
Step 1: Since PQ is parallel to BC, use the basic proportionality theorem. Step 2: Write the ratio of the divided sides. AP/PB = AQ/QC Answer: The line divides the two sides in the same proportion.
When do you use the basic proportionality theorem?
Answer
Use it when a line is parallel to one side of a triangle and cuts the other two sides at distinct points. Example: If PQ ∥ BC in triangle ABC, then AP/PB = AQ/QC. This helps compare the two divided si…
Solve: In triangle ABC, line PQ is parallel to BC. If AP = 3 cm, PB = 6 cm, and AQ = 4 cm, find QC.
Answer
Step 1: Use the basic proportionality theorem. AP/PB = AQ/QC Step 2: Substitute the values. 3/6 = 4/QC Step 3: Simplify 3/6 = 1/2. So, 1/2 = 4/QC Step 4: Cross-multiply. QC = 8 cm Answer: QC = 8 cm…
Why does the basic proportionality theorem work?
Answer
Count the triangles formed by drawing the two extra segments. Triangles APQ, PQB, and PQC are used in the proof. Because the line is parallel to BC, the smaller triangles have equal heights where need…
Solve: In triangle PQR, if PS/SQ = PT/TR, what can you conclude about ST and QR?
Answer
Step 1: Recognise the converse of the basic proportionality theorem. Step 2: If a line divides two sides of a triangle in the same ratio, it is parallel to the third side. Step 3: Here, the line throu…
What is the key idea behind the converse of the basic proportionality theorem?
Answer
If the two sides of a triangle are divided in the same ratio, then the joining line must be parallel to the third side. A common way to prove this is by the indirect method. This result is useful when…
Solve: In triangle ABC, if the bisector of angle C meets AB at E, write the ratio formed on AB.
Answer
Step 1: Apply the angle bisector theorem. Step 2: The bisector of an angle divides the opposite side in the ratio of the remaining two sides. AE/EB = CA/CB Answer: AE/EB = CA/CB…
Solve: In triangle ABC, angle C is bisected at E on AB. If CA = 10 cm and CB = 15 cm, and AE = 8 cm, find EB.
Answer
Step 1: Use the angle bisector theorem. AE/EB = CA/CB Step 2: Substitute the values. 8/EB = 10/15 Step 3: Simplify 10/15 = 2/3. So, 8/EB = 2/3 Step 4: Cross-multiply. 2 × EB = 3 × 8 2EB = 24 EB = 12 c…
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