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The side B C of a triangleA B C is produ...

The side `B C` of a triangle`A B C` is produced on both sides. Show that the sum of the exterior angles so formed is greater than `/_A` by two right angles.

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To solve the problem, we need to show that the sum of the exterior angles formed by extending the side BC of triangle ABC is greater than angle A by two right angles (180 degrees). Here’s a step-by-step solution: ### Step 1: Understand the Triangle and Extend the Side We have triangle ABC, and we extend the side BC on both sides. This creates two exterior angles, which we will call angle 1 and angle 2. ### Step 2: Apply the Angle Sum Property of a Triangle According to the angle sum property of a triangle: \[ ...
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The side B C of a A B C is produced on both sides. Show that the sum of the exterior angles so formed is greater than /_A by two right angles.

The side B C of a A B C is produced on both sides. Show that the sum of the exterior angles so formed is greater than /_A by two right angles.

If the side B C of A B C is produced on both sides, then write the difference between the sum of the exterior angles so formed and /_A .

If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.

If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is (a) 90^0\ (b) 180^0 (c) 270^0 (d) 360^0

Alternate sides of a hexagon are produced to meet so as to form a star-shaped figure. Show that the sum of a angles at vertices of the star is equal to 4-right angles.

Which of the following statements are true (T) and which are false (F): Sum of the three angles of a triangle is 180^0 A triangle can have two right angles. All the angles of a triangle can be less than 60^0 All the angles of a triangle can be greater than 60^0 All the angles of a triangle can be equal to 60^0 A triangle can have two obtuse angles. A triangle can have at most one obtuse angles. In one angle of a triangle is obtuse, then it cannot be a right angled triangle. An exterior angle of a triangle is less than either of its interior opposite angles. An exterior angle of a triangle is equal to the sum of the two interior opposite angles. An exterior angle of a triangle is greater than the opposite interior angles

The side B C\ of a triangle A B C is produced, such that D is on the ray B Cdot The bisector of /_A meets B C in L as shown in Figure. Prove that /_A B C+/_A C D=2/_A L C

(Exterior Angle Theorem): If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles. GIVEN : A triangle A B C,D is a point of B C produced, forming exterior angle /_4. TO PROVE : /_4=/_1+/_2 i.e. , /_A C D=/_C A B+/_C B Adot

Which of the following statements are true (T) and which are false (F)? (i) Sum of the three sides of a triangle is less than the sum of its three altitudes. (ii) Sum of any two sides of a triangle is greater than twice the median drawn to the third side. (iii) Sum of any two sides of a triangle is greater than the third side. (iv) Difference of any two sides of a triangle is equal to the third side. (v) If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it. (vi) Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.

RD SHARMA ENGLISH-CONGRUENT TRIANGLE -All Questions
  1. Sides B C ,C A and BA of a triangle A B C are produced to D ,Q ,P resp...

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  2. A B C is a triangle and D is the mid-point of B C . The perpendiculars...

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  3. The side B C of a triangleA B C is produced on both sides. Show that t...

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  4. P is a point equidistant from two lines l and m intersecting at a poin...

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  5. If two parallel lines are intersected by a transversal, prove that ...

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  6. If A B C is an isosceles triangle such that A B=A C and A D is an alti...

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  7. If PS is the bisector of /Q P R and P T|Q R . Show that /T P S=1/2(/Q...

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  8. Of all the line segments that can be drawn to a given line, from a ...

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  9. A triangle A B C is right angled at A. AL is drawn perpendicular to B...

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  10. The sum of any two sides of a triangle is greater than the third sid...

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  11. In Figure AB||DC , if x=(4y)/3 and y=(3z)/8, find /B C D ,/A B C and /...

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  12. A B is a line segment and line l is its perpendicular bisector. If ...

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  13. A B C is a triangle in which /A=72^0 , the internal bisectors of angle...

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  14. AB is a line-segment. P and Q are points on opposite sides of AB suc...

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  15. If one angle of a triangle is equal to the sum of the other two, sh...

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  16. Suppose line segments A B and C D intersect at O in such a way that A ...

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  17. Two angles of a triangle are equal and the third angle is greater th...

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  18. If D is the mid-point of the hypotenuse A C of a right triangle A B C ...

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  19. In triangle A B C ,/B=45^0,/C=55^0 and bisector of /A meets B C at ...

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  20. A B is a line segment, A X and B Y are two equal line segments drawn o...

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