You can achieve good scores in math every time if you Practice. For your benifit we have come up with Important questions for all the grades. These sets of important questions in all the subjects will help you in dealing with difficult topics too.
Important questions based on NCERT syllabus for Chapter 7 - Triangles:
Question 1: In Fig. X and Y are two points on equal sides AB and AC of a ΔABC such that AX = AY. Prove that XC = YB.
In Δs AXC and AYB, we have
AX = AY [Given]
∠A = ∠A [Common angle]
AC = AB [Given]
ΔAXC ≅ ΔAYB [SAS congruence criterion]
⇒ XC = YB [Since corresponding parts of congruent triangles are equal]
Question 2: 6. In Fig., AB || DC. If x = 43 y and y = 38 z, find ∠BCD, ∠ABC and ∠BAD?
Solution: Since AB || DC and transversal BD intersects them at B and D respectively.
∠ABD = ∠BDC [Alternate angles]
And ∠CBD = ∠ADB
∠BDC = x∘ and y = 36∘
∠ABD =x∘ and ∠ADB = 36∘ (Given)
But, it is given that,
x = 4/3y and y= 3/8 z
x = 4/3 × 36 and 36 = 3/8z
x = 48 and z = 36 × 8/3 = 96
Now, in BAD, we have
∠BAD + ∠ADB + ∠ABD = 180∘
∠BAD + 36∘ + x∘ = 180∘
∠BAD + 36∘ + 48∘ = 180∘
∠BAD = 96∘
Thus, ∠BCD = z∘ = 96∘,
∠ABC = x∘ + y∘= 48∘ + 36∘ =84∘ and ∠BAD = 96∘
Question 3: 11. The sum of two angles of a triangle is 80∘ and their difference is 20∘. Find all the angles.
Solution: Let ABC be the triangle
∠A + ∠B = 80∘ and ∠A - ∠B =20∘
Adding the two equations, we get
∠A = 50∘ and ∠B = 30∘
We know that,
∠A + ∠B + ∠C = 180∘ [Angle sum property]
⇒ ∠C = 100∘