Blog

Parin Sir > Quantitative Aptitude (Maths) > Triangle > Examples of Triangle > Examples of Triangle

Examples of Triangle

August 7, 2020
Category: Examples of Triangle

No Comments

(1) Calculate $\angle$ ABC and $\angle$ BAC.

Soln. $\angle$ ABC + 100⁰ = 180⁰ ( straight line ) $\angle$ ABC = 80⁰

$\angle$ BAC = 180⁰ – ( 60⁰ + 80⁰ ) = 180⁰ – 140⁰ = 40⁰

( sum of angles of a triangle = 180^o )

(2) Calculate $\angle$ ACD and $\angle$ CDA.

Soln. $\angle$ ABC is isosceles ( AC = BC ) $\therefore$ $\angle$ ABC = 40⁰

$\angle$ ACD = $\angle$ ABC + $\angle$ BAC = 80^o ( exterior angle )

$\therefore$ $\angle$ CDA = 180⁰ – ( $\angle$ ACD + $\angle$ CAD ) = 180⁰ – ( 80⁰ + 30⁰ ) = 70⁰

(3) ABCD is a quadrilateral where $\angle$ D = 70^o, $\angle$ C = 80^o. Bisectors of $\angle$ A and $\angle$ B meet at P. Calculate $\angle$ APB.

Soln. $\angle$ A + $\angle$ B = 360⁰ – ( 70⁰ + 80⁰ ) = 360⁰ – 150⁰ = 210⁰.

$\therefore \frac{\angle A + \angle B}{2}$ = 105⁰ $\therefore$ $\angle$ APB = 180⁰ – 105⁰ = 75⁰.

(4) AB = AD, BC = CD, $\angle$ BAD = 100^o and $\angle$ DBC = 50^o. Calculate $\angle$ ADC and $\angle$ BDC.

Soln. $\Delta$ BCD is an isosceles triangle ( BC = CD )

$\therefore$ $\angle$ BDC = 50⁰

$\therefore$ In $\Delta$ ABD, AD = AB

$\therefore$ $\angle$ ABD = $\angle$ ADB

Now, in $\Delta$ ABD ,

$\angle$ ABD + $\angle$ ADB + $\angle$ BAD = 180⁰

2 $\angle$ ABD + 100⁰ = 180⁰

$\therefore$ 2 $\angle$ ABD = 80⁰

$\therefore$ $\angle$ ABD = 40⁰ = $\angle$ ADB

$\therefore$ $\angle$ ADC = $\angle$ ADB + $\angle$ BDC = 40⁰ + 50⁰ = 90⁰.

(5) In a $\Delta$ ABC, AB = 10, BC = 2 $\sqrt{97}$ , AC = 12. Find the length of median AD. If G is the centroid, find l ( GA ) and l ( GD ).

By Apollonius theorem, we have,

AB² + AC² = 2 $\times$ AD² + 2 BD²

10² + 12² = 2 $\times$ AD² + 2 $\times$ ( $\sqrt{97}$ )²

244 – 194 = 2 $\times$ AD²

50 = 2 $\times$ AD²

AD = 5

G divides AD in the ratio 2 : 1, hence GA = $\frac{2}{3}\times$ AD = $\frac{2}{3}\times$ 5 = $\frac{10}{3}$

and GD = $\frac{1}{3}\times$ 5 = $\frac{5}{3}$ .

Blog

Examples of Triangle

Best of Luck…

Leave a Reply Cancel reply