Question

construct triangleabc in which bc=6.3cm angle b= 75 and ab+ac=9cm
prove that the sum of measure of all angles of a triangle is 180​

Answer 1

Step-by-step explanation:

1. Draw a line BC=6cm

2. Construct 30

o

at B. Extend BP.

3. Take 3.1cm on compass, cut an arc on BP. Join CX.

4. Take perpendicular bisector of CX. It intersects with BP at A. Join AC

Answer 2

Given:

(1) construct triangle ABC in which bc=6.3cm angle b= 75 and ab + ac=9cm

(2) prove that the sum of measure of all angles of a triangle is 180​°

Here the solution of (1)

Diagram are in attachment

(1)  c=6.3cm angle b= 75 and ab + ac=9cm

(1) Draw a base BC of length 6.3 cm

(2) Draw angle B=75°  

(3) Open the compass for length AB+AC=9cm

(4) Cot an arc on ray BX at D

(5) Join CP

(6) Draw ⊥ bisector of CD.

(7) Mark point A where ⊥ bisector cut BD.

(8) Join AC

Here solution of (2)

A triangle ABC.

To prove :

∠A+∠B+∠C=180°

∠1+∠2+∠3=180°

Construction :

Through A, draw a line l parallel to BC.

Proof :

Since l∥BC. Therefore,

∠2=∠4 -(1)

And, ∠3=∠5   -(2)

adding  (1) and (2)

Therefore, ∠2+∠3=∠4+∠5

∠1+∠2+∠3=∠1+∠4+∠5  [adding∠1bothSide]

∠1+∠2+∠3=180°

Diagram are in attachment