Congruent Figures Figures are congruent if they are exactly the same size and shape. These figures are congruent because one figure can be translated onto.

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Presentation transcript:

Congruent Figures Figures are congruent if they are exactly the same size and shape. These figures are congruent because one figure can be translated onto the other figure.

Congruent Figures Now look at these two figures: They are also congruent because one figure can be rotated onto the other.

Congruent Figures Finally look at these two figures: They are also congruent because one figure can be reflected onto the other figure.

Congruent Polygons In general we can say that polygons are congruent if the following two conditions are true: The angles in one figure are the same as the angles in the other figure and are in the same order either clockwise or anticlockwise. The lengths of the sides between corresponding pairs of adjacent angles are the same for both figures. Therefore to determine congruence we need to know all of the angles and the lengths of all but one of the sides. Not very practical!!

Congruent Triangles As triangles have only three sides there are four rules that allow us to determine whether two triangles are congruent with only three pieces of information: (SSS) – If all of the sides on one triangle are the same as the sides on another then the triangles are congruent. 5 3 2

Congruent Triangles As triangles have only three sides there are four rules that allow us to determine whether two triangles are congruent with only three pieces of information: (SAS) – If two sides and the angle between them are equal then the two triangles are congruent. 5 4 20º

Congruent Triangles As triangles have only three sides there are four rules that allow us to determine whether two triangles are congruent with only three pieces of information: (AAS) – If two angles are equal and a side on one triangle is the same length as a corresponding side on the other triangle then the triangles are congruent. 7 20º 100º

Congruent Triangles As triangles have only three sides there are four rules that allow us to determine whether two triangles are congruent with only three pieces of information: (RHS) – If both triangles are right angled, have equal hypotenuses and another equal side then they are congruent. 6 2

Congruent Triangles Before we prove congruence between triangles we must practice our four congruent rules: Eg.1 Are these two triangles congruent? If so, which test confirms it? 4 70° 80° 5 7 A B C D E F

Congruent Triangles Before we prove congruence between triangles we must practice our four congruent rules: Eg.2 Are these two triangles congruent? If so, which test confirms it? 4 70° 80° 5 7 A B C D E F

Congruent Triangles To use the properties of congruence to help us solve problems we first have to prove that one triangle is congruent to another: e.g. Find the value of x in the diagram below giving reasons for your answer: 4 70° 80° 5 7 x A B C D E F

Congruent Triangles e.g. Find the value of x in the diagram below giving reasons for your answer: 4 100° 6 xº A B C D