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Fill in the blanks in the following so that each of the following statements is true.
(i) Sides opposite to equal angles of a triangle are .......
(ii) Angle opposite to equal sides of a triangle are .......
(iii) In an equilateral triangle all angles are .......
(iv) In a ` A B C` if `/_A=/_C ,` then `A B=\ ` .....
(v) If altitudes `C E\ a n d\ B F` of a triangle `A B C` are equal, then `A B=` ........
(vi) In an isosceles triangle `A B C` with `A B=A C ,` if `B D\ a n d\ C E` are its altitudes, then `B D` is .......... `C E`.
(vii) In right triangles `A B C\ a n d\ D E F ,` if hypotenuse `A B=E F` and side `A C=D E ,` then ` A B C\ ~=` ....

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Theorem 7.3 : The sides opposite to equal angles of a triangle are equal.

Theorem 7.2 : Angles opposite to equal sides of an isosceles triangle are equal.

Show that in an isosceles triangle, angles opposite to equal sides are equal.

By giving a counter example, show that the following statement is not true: p : if all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.

In an isosceles triangle, prove that the angles opposite to equal sides are equal.

If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

A triangle whose two sides are equal is called (a) an acute triangle (b) a scalene triangle (c) an isosceles triangle (d) an equilateral triangle

In a triangle the greater angle has the longer side opposite to it.

Angle A ,\ B ,\ C of a triangle A B C are equal to each other. Prove that A B C is equilateral.

D and E are points on equal sides A B and A C of an isosceles triangle A B C such that A D=A E . Prove that B ,C ,D ,E are concylic.

RD SHARMA ENGLISH-CONGRUENT TRIANGLE -All Questions
  1. A B C D is a square, X\ a n d\ Y are points on sides A D\ a n d\ B C r...

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  2. Which of the following statements are true (T) and which are false ...

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  3. Fill in the blanks in the following so that each of the following st...

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  4. In a A B C ,\ if /A=45^0\ a n d\ /B=70^0dot Determine the shortest ...

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  5. In a A B C , if /A=50^0\ a n d\ /B=60^0 , determine the shortest a...

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  6. In Figure, P Q > P R. Q S\ a n d\ R S are the bisectors of / Q and /R ...

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  7. In Figure, sides L M\ a n d\ L N OF /\ LMN are extended to P\ a n d\ Q...

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  8. In Figure, P Q=P Rdot Show that P S > P Q

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  9. In Figure, A B > A C. Show that A B > A D.

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  10. If D is any point on the base B C produced, of an isosceles tria...

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  11. In Figure, if A D is the bisector of L A , show that: A B > B D (ii) ...

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  12. Show that in a right angled triangle, the hypotenuse is the longest...

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  13. In Figure, A C > A B and A D is the bisector of / A . Show that A D C ...

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  14. Show that the sum of the three altitudes of a triangle is less than...

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  15. Prove that any two sides of a triangle are together greater than tw...

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  16. Prove that the perimeter of a triangle is greater than the sum of it...

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  17. Show that the difference of any two sides of a triangle is less than...

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  18. In Figure, P Q R is a triangle and S is any point in its interior, s...

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  19. In P Q R , S is any point on the side Q R . Show that P Q+Q R+R P ...

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  20. In Figure, A P\ |l\ a n d\ P R > P Q . Show that A R > A Q.

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