Answer
Verified
415.2k+ views
In this question we have to use construction and use the properties of parallel lines . Use substitution of angles of the triangle with the angles on the straight line to get to the final answer .
Complete step-by-step answer:
Construct a straight line EF passing through A parallel to the base BC of the triangle .
$\angle ABC = \angle EAB$ ( alternate angles are equal as lines BC and EF are parallel )
$\angle BCA = \angle FAC$ ( alternate angles )
Now we know that the sum of all linear angles is $180^\circ $
Therefore $\angle EAB + \angle BAC + \angle FAC = 180^\circ $
By substitution of angles from above , we get
$\angle ABC + \angle CAB + \angle ACB = 180^\circ $
Hence proved the sum of all angles of a triangle is $180^\circ $
Note –In such questions construction becomes necessary to prove the desired result. We should remember the properties of parallel lines to get the desired answer .
Complete step-by-step answer:
Construct a straight line EF passing through A parallel to the base BC of the triangle .
$\angle ABC = \angle EAB$ ( alternate angles are equal as lines BC and EF are parallel )
$\angle BCA = \angle FAC$ ( alternate angles )
Now we know that the sum of all linear angles is $180^\circ $
Therefore $\angle EAB + \angle BAC + \angle FAC = 180^\circ $
By substitution of angles from above , we get
$\angle ABC + \angle CAB + \angle ACB = 180^\circ $
Hence proved the sum of all angles of a triangle is $180^\circ $
Note –In such questions construction becomes necessary to prove the desired result. We should remember the properties of parallel lines to get the desired answer .
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE