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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.

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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…

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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…

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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…

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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…

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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…

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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…

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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…