Congruent shapes are exactly the same shape and size. For triangles, you do not need to check everything. Any one of four conditions is enough.
SSS: all three sides are equal. SAS: two sides and the angle between them are equal. ASA (or AAS): two angles and a corresponding side are equal. RHS: both have a right angle, equal hypotenuses and another equal side. Three equal angles are not enough, because the triangles could be different sizes, which is similarity.
Worked example
Two triangles have sides 5, 7 and the angle between them 40° in both. Are they congruent?
- Two sides and the included angle are equal.
- That is the SAS condition.
Answer:Yes, by SAS.
Key words
- congruent
- identical in shape and size
- SAS
- side, angle (between), side
- RHS
- right angle, hypotenuse, side
Practise this
New questions every time.
Common Core-referenced: HSG-SRT.B.5