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Q) Sides AB, BC and the median AD of ∆ ABC are respectively proportional to sides PQ, QR and the median PM of another∆ PQR. Prove that ∆ ABC ~ ∆ PQR Ans: Given that, In Δ ABC and Δ PQR, Since AD is median of BC, hence BC = 2BD Similarly, PM is median of […]
triangles
Q) E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ∆ ABE ~ ∆ CFB. Ans: Given: ABCD is a parallelogram and line AD is extended to point E. Line BE intersects CD at point F To Prove: △ ABE ~ △ CFB
E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Read More »
Q) In 𝛥ABC, D, E and F are midpoints of BC,CA and AB respectively. Prove that △ 𝐹𝐵𝐷 ∼ △ DEF and △ DEF ∼ △ ABC Ans: (i): Prove that △ 𝐹𝐵𝐷 ∼ △ DEF: Let’s start from comparing triangles △ FBD and △ DEF. Since by midpoint theorem, The line segment in a
Q) In 𝛥ABC, P and Q are points on AB and AC respectively such that PQ is parallel to BC. Prove that the median AD drawn from A on BC bisects PQ. Ans: Step 1: Let’s start from comparing triangles △ APR and △ ABD. Here we have: ∠ APR = ∠ ABD (corresponding
In 𝛥ABC, P and Q are points on AB and AC respectively such that PQ is parallel to BC. Read More »
Q) Triangle is a very popular shape used in interior designing. The picture given above shows a cabinet designed by a famous interior designer. Here the largest triangle is represented by △ ABC and smallest one with shelf is represented by △ DEF. PQ is parallel to EF. (i) Show that △ DPQ ∼ △ DEF.
Q) In the given figure, EA/EC = EB/ ED , prove that ΔEAB ~ ΔECD Ans: Step 1: It is given that: ∴ by cross multiplying, we can say that: Step 2: Let’s look at Δ EAB and Δ ECD: ∠ AEB = ∠ DEC (∵ Vertically Opposite Angles) Step 3: Let’s compare Δ EAB
In the given figure, EA/EC = EB/ ED , prove that ΔEAB ~ ΔECD Read More »
Q) Prove that the tangents drawn at the end points of a chord of a circle makes equal angles with the chord. Ans: Let’s start by making a diagram for the question: Here, we have circle with Centre O and PQ is a chord. From point R, two tangents are drawn at end points of
Prove that the tangents drawn at the end points of a chord of a circle makes equal Read More »
Q) A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the
A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs Read More »
Q) In the given figure, AB and CD are tangents to a circle centred at O. Is angle BAC = angle DCA ? Justify your answer. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Step 1: Let’s connect center O with points A and C Step 2: Since BA is the tangent to the circle and
Q) In the given figure, PQ is tangent to a circle centred at O and ∠BAQ = 30°; show that BP = BQ. Ans: Here, We need to prove that BP = BQ, it means we need to get ∠ BQP = ∠ BPQ Step 1: Let’s start with given diagram. Since AB is a straight