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The angles opposite to equal sides of an...

The angles opposite to equal sides of an isosceles triangle are ..........

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

Angles opposite to two equal sides of a triangle are equal.

Prove that the medians to the two equal sides of an isosceles triangle are equal.

Prove that the angle opposite to the equal sides of an equilateral triangle are equal.

Fill in the blanks in the following so that each of the following statements is true Sides opposite to equal angles of a triangle are ....... Angle opposite to equal sides of a triangle are ....... In an opposite to equal sides of a triangle are ....... In a A B C if /_A=/_C , then A B= ..... If altitudes C E a n d B F of a triangle A B C are equal, then A B= ........ 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 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 ~= ....

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

Which of the following statements are true (T) and which are false (F): Side opposite to equal angles of a triangle may be unequal. Angle opposite to equal sides of a triangle are equal. The measure of each angle of an equilateral triangle is 60^0 If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles. The bisectors of two equal angles of a triangle are equal. If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. The two altitudes corresponding to two equal sides of a triangle need not be equal. If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent. Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.

ISOSCELES TRIANGL.E A triangle whose two sides are equal is called an isosceles triangle.

Prove that the perpendiculars drawn from the vertices of equal angles of an isosceles triangle to the opposite sides are equal.

RS AGGARWAL-TRIANGLES-EXERCISE 16A
  1. Take three noncollinear points A, B and C on a page of your notebook. ...

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  2. The measures of two angles of a triangle are 72^(@) and 58^(@). Find t...

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  3. The angles of a triangle are in the ratio 1:3:5. Find the measure of e...

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  4. One of the acute angles of a right triangle is 50^(@). Find the other ...

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  5. One of the angles of a triangle is 110^(@) and the other two angles ar...

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  6. If one angle of a triangle is equal to the sum of other two, show that...

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  7. In a A B C ,\ if\ 3/\ \ A=4/\ B=6/\ C , calculate the angles.

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  8. Look at the figure given below. State triangle whether it is acute, ri...

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  9. In the given figure. State triangle whether it is scalene, isosceles o...

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  10. Draw a Delta ABC. Take a point D on BC. Join AD How many triangles do ...

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  11. Can a triangle have: Two right angles? (ii) Two obtuse angles? Two acu...

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  12. A triangle has ...... sides, ...... angles and ...... vertices.

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  13. The sum of the angles of a triangle is .......

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  14. The sides of a scalene triangle are of ........... lengths.

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  15. Each angle of an equilateral triangle measures .......

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  16. The angles opposite to equal sides of an isosceles triangle are .........

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  17. The sum of the lengths of the sides of a triangle is called its .........

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