PowerPoint Presentation: MATHEMATICS PRESENTATION
Triangles : Triangles
Triangles: Triangles A CLOSED FIGURE FORMED BY THREE INTERSECTING LINES IS CALLED A TRIANGLE. A TRIANGLE HAS THREE SIDES, THREE ANGLES AND THREE VERTICES . ANGLES OPPOSITE TO EQUAL SIDES OF A TRIANGLE ARE EQUAL. SIDES OPPOSITE TO EQUAL ANGLES OF A TRIANGLE ARE EQUAL.
Scalene Triangle: Scalene Triangle Has no congruent sides. The SIDES and ANGLES of a Scalene Triangle have unequal measurements. A B C
Isosceles Triangle: Isosceles Triangle Has at least two congruent sides. Angles opposite to equal sides of an isosceles triangle are equal. The sides opposite to equal angles of an isosceles triangle are equal. A B C D E F L M N
Equilateral Triangle: Equilateral Triangle Has three congruent sides. Each angle of an equilateral triangle is of 60 degree and all the sides are of equal measurements. P Q R
TWO SQUARES OF THE SAME SIDES ARE CONGRUENT. : TWO SQUARES OF THE SAME SIDES ARE CONGRUENT. TWO CIRCLES OF THE SAME RADII ARE CONGRUENT .
PowerPoint Presentation: Congruent Triangles
EXAMPLE: : EXAMPLE: Two triangles are congruent if the sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle. 2m 2m
Congruence of Triangles: Congruence of Triangles CONGRUENT MEANS EQUAL IN ALL RESPECT OR FIGURES WHOSE SHAPE AND SIZE ARE BOTH THE SAME. THEY MAY BE FLIPPED AND/OR ROTATED.
Example:: Example: If two triangles ABC and PQR are congruent under the correspondence A P, B Q, and C R, then symbolically, it is expressed as ABC = PQR
Criteria for Congruence of Triangles: Criteria for Congruence of Triangles ( SAS CONGRUENCE RULE ): Two triangles are congruent if two sides and the included angle of one triangle are equal to the sides and the included angle of the other triangle.
Example:: Example: ABC is congruent to DEF by the SAS congruence rule. C 4cm 12cm 12cm 4cm 90 90 A B C D E F
PowerPoint Presentation: (ASA CONGRUENCE RULE): Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle . Example: Both have the same measurements of the angles and the side included. 60 90 10cm 90 60 10cm
(A) (B): ( A) (B) (AAS CONGRUENCE RULE): Two triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal . Example: ABC is congruent to DEF. D E F X Y Z 90 90 40 40 2cm 2cm
(SSS CONGRUENCE RULE): If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.: (SSS CONGRUENCE RULE): If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent. 4cm 4cm 6cm 6cm 5cm 5cm Example:
(RHS CONGRUENCE RULE): If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.: (RHS CONGRUENCE RULE): If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent . 6cm 6cm 8cm 8cm Example:
Inequalities in a triangle : Inequalities in a triangle THEOREMS : If two sides of a triangle are unequal, the angle opposite to the longer side is larger. In any triangle, the side opposite to the larger (greater) angle is longer. The sum of any two sides of a triangle is greater than the third side.
MADE BY: nikita class 9th-A: MADE BY: nikita class 9 th -A THANK YOU