But one is just a bigger,Ī blown-up version of the other one. Of YZ to the length of BC, we also multiplied by 3. To the length of AB, which is the corresponding side, So all of their correspondingĪngles are the same. Angle BCA is congruentĬongruent to angle XYZ. So the angle right here, angleīAC, is congruent to angle YXZ. One, all of their correspondingĪngles are the same. Relationship between these two triangles. They aren't congruent, that they have very different Without knowing at least one side, we can't be sure if two triangles are congruent.ĪBC to triangle XYZ, it's pretty clear that This is not enough information to decide if two triangles are congruent!īecause the triangles can have the same angles but be different sizes: 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.ĪAA means we are given all three angles of a triangle, but no sides. It doesn't matter which leg since the triangles could be rotated. The same length for one of the other two legs. It means we have two right-angled triangles with HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs") This one applies only to right angled-triangles! If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent. 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.ĪAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side 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.ĪSA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal. SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL. But we don't have to know all three sides and all three angles. Two triangles are congruent if they have: exactly the same three sides and exactly the same three angles.
They don't have to be on similar sized lines.
They don't have to point in the same direction. Congruent? Why such a funny word that basically means "equal"? Maybe because they are only "equal" when placed on top of each other. After any of those transformations (turn, flip or slide), and the shape still has the same size, area, angles and line lengths, then the shape is congruent to the other. If one shape can become another using Turns, Flips and/or Slides, then the shapes are Congruent. This proves the triangle angle bisector theorem: the angle bisector of one angle of a triangle divides the opposite side of the triangle into segments proportional to the lengths of the other two sides of the triangle.Say you have 2 shapes.
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