Shapes which are congruent

Approaching a geometric problem. Adding auxilliary lines. More construction lines. Exploring quadrilaterals. Properties of quadrilaterals. Exploring congruence. Developing the congruence tests. Looking beyond the lines. Visualising relationships. Writing a proof.

Proving Pythagoras' theorem. Exploring circles. Explore, predict, confirm. Assessment approaches. Practical tasks. Working collaboratively. Pen and paper. Creative construction. Assessment design. Changing direction. Literacy questions. Find the error. Geometry games. Circle geometry investigations. To determine if two polygons are congruent, find the length of all of the sides and all of the angles.

If all of them are the same, the two polygons are congruent. If anything is different, they are not going to be congruent. For example, one rectangle has 2 sides that are 4 inches and 2 sides that are 8 inches. All of the angles are 90 degrees. If another rectangle has 2 sides that are 4 inches and 2 sides that are 8 inches as well, the rectangles are congruent. If a rectangle has 2 sides that are 5 inches and two sides that are 3 inches, and another one has 2 sides that are 4 inches and 2 sides that are 7 inches, these rectangles are not congruent.

Even though they both have the same angles, they do not have the same side lengths and therefore are not the same. Picture a rectangle with horizontal sides 6 inches long and vertical sides 2 inches long. For example, check out these two triangles:. Here we have two equal acute angles, shown by the letter A.

There are also two equal obtuse angles, shown by the letter B. The side between angles A and B are marked by two dashes, showing that these sides are also equal. Therefore, we know that these triangles follow the ASA Postulate. Therefore, they are congruent.

For the SAS Postulate, the two triangles need to have two identical sides and an identical angle. The identical angle should be positioned between the identical sides. In this example, the triangles have listed measurements for comparison. The long side of each triangle has a measurement of 5, and the shorter side has a measurement of 3 in both triangles.

The angle between these sides is degrees. Because of this, we can surmise that the triangle follows the SAS Postulate. The SSS Postulate simply states that all the sides of the two triangles are equal. So, if you can measure each side of the triangle and end up with three equal corresponding sides, you know that the two triangles are congruent. Check out the following example, and notice that all three sides have equal lengths:. With the measurements of the three sides in the first triangle corresponding to the measurements of the second triangle, we can use the SSS Postulate to determine that the triangles are congruent.

With the AAS Theorem, you can prove that two triangles are congruent by checking the measurement of two angles.