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Transcript
How To Identify if Triangles are Congruent Outcome: E1 make and apply informal deductions about the minimum and sufficient conditions to guarantee the uniqueness of a triangle and the congruency of two triangles Two triangles are congruent if they have: •exactly the same three sides and •exactly the same three angles. But we don't have to know all three sides and all three angles ...usually three out of the six is enough. Methods for identifying whether two triangles are congruent: Method (Postulate) Example S-S-S This stands for "side, side, side" and means that we have two triangles with all three sides equal. Proof If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. S-A-S This stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal. If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent. A-S-A This stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal. If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent. Method (Postulate) Example HL This stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs") Proof If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent. It means we have two right-angled triangles with: •the same length of hypotenuse and •the same length for one of the other two legs. DO NOT USE A-A-A!!! (Angle-Angle-Angle) AAA means we are given all three angles of a triangle, but no sides. This is not enough information to decide if two triangles are congruent! Because the triangles can have the same angles but be different sizes: