Side Side Side(SSS) Congruence : Two triangles are congruent if the three sides of one triangle are equal to the corresponding three sides of the other triangle.

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.

Prove that Two right triangles are congruent if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and one side of the other triangle.

If the ex-radii of a triangle are in H.P.,then the corresponding sides are in

Two triangles are congruent if two sides and the included angle of one are equal to the corresponding sides and the included angle of the other triangle. GIVEN : Two triangles A B C and D E F such that A B=D E ,A C=D F and /_A=/_D PROVE : A B C~= D E F Figure

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

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

Theorem 7.4 (SSS congruence rule) : If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

In two right triangles, one side and an acute angle of one triangle are equal to one side and the corresponding acute angle of the other triangle. Prove that the two triangles are congruent.

In two right triangles, one side and an acute angle of one triangle are equal to one side and the corresponding acute angle of the other triangle. Prove that the two triangles are congruent.