Q) Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two wires cross. i. What is […]
Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. Read More »
Q) If in Δ ABC, AD is median and AE ⊥ BC, then prove that AB2 + AC2 = 2 AD2 + BC2 Ans: Step 1: Let’s make a diagram for the question: Step 2: In Δ ABE, ∠ AEB is 900, ∴ by Pythagoras theorem: AB2 = AE2 + BE2 …….. (i) Similarly, In Δ
If in Δ ABC, AD is median and AE ⊥ BC, then prove that AB2 + AC2= 2 AD2 +1/2 BC2 Read More »
Q) An arc of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the corresponding major sector. (Use π = 3·14) Ans: The Area of an arc making θ angle at centre is given by: A = π r 2 x given the values as
Q) In the given figure, Δ FEC ≅ Δ GDB and ∠ 1 = ∠ 2. Prove that Δ ADE ~ Δ ABC. Ans: Step 1: Since Δ FEC ≅ Δ GDB ∴ BD = CE (by CPCT) Step 2: Since ∠ 1 = ∠ 2 ∴ AD = AE (since sides
In the given figure, Δ FEC ≅ Δ GDB and ∠ 1 = ∠ 2.Prove that Δ ADE ~ Δ ABC. Read More »
Q) In the given figure, ∆ AHK ~ ∆ ABC. If AK = 8 cm, BC = 3.2 cm and HK = 6.4 cm, then find the length of AC. Ans: Step 1: Since Δ AHK ~ Δ ABC (given) Therefore, ∴ AC = Step 2: It is given
In the given figure, ∆ AHK ~ ∆ ABC. If AK = 8 cm, BC = 3.2 cm and HK = 6.4 cm, Read More »
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
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.(ii) If DP=