Grade 4 Congruence Rules Use the basic congruence

Grade 4 Congruence Rules Use the basic congruence criteria for triangles. If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Congruent Congruence Side Angle Opposite

How to identify congruent triangles Congruent shapes are identical but can be reflected, rotated or translated. There are 4 rules to prove that triangles are congruent 1)SSS – if all 3 sides on one triangle have a matching side on another triangle. c a a b b c

How to identify congruent triangles Congruent shapes are identical but can be reflected, rotated or translated. There are 4 rules to prove that triangles are congruent 2) SAS – If a side, the angle next to it and the side next to that have a matching sequence on another triangle. a C a b b C

How to identify congruent triangles Congruent shapes are identical but can be reflected, rotated or translated. There are 4 rules to prove that triangles are congruent 3) ASA – If a side, the angle OPPOSITE to it and another angle have a matching sequence on another triangle. a a C A A C

How to identify congruent triangles Congruent shapes are identical but can be reflected, rotated or translated. There are 4 rules to prove that triangles are congruent 4) RHS – If both triangles have a right angle, an equal hypotenuse and any other side is a equal. R H a H R

Example Prove that these triangles are congruent using one of the rules for congruency: 3 cm There are 2 angles and 1 side that match up but they need to be in a sequence. 76 o 7 cm 76 o and 7 cm are a pair of opposites that both triangles have and they both have a 38 o angle. This is the ASA rule. 38 o 76 o 6 cm 7 cm 38 o

Practice Each pair of shapes may be congruent. State which rule for congruency can be used to prove this and give reasons if they are. 5 cm 1) 82 o and 9 cm are opposite 12 cm o 82 and both have 38 o. ASA. 2) 1) 9 cm o 2) Isosceles triangles so both 38 38 o 6 cm 9 cm sides are 12 cm and they share an angle of 120 o. SAS o 82 3) Both have a right angle and equal hypotenuse. The corresponding side of 3 cm 3 c m 4) 3) is also equal. RHS. 4) These are not congruent – although it looks like RHS, 5 cm 4 cm 3 cm the 4 cm side is not labelled as the same side on each triangle. 120 o 12 cm 4 cm 7 cm

Reasoning. In the Gherkin there are many triangular panes of glass. Bob says that 2 particular panes are congruent because they have 2 angles and a side the same. Is he correct? Explain why. 2 angles and a side could fit in to the ASA rule but the side and angle need to be opposite. If you have 2 angles in a triangle, you can find the third so there would have to be a pair of opposites. Bob is correct.