Congruence

Congruence

Congruency: When something is exactly the same. the symbol for congruency is: an = sign with ~ on the top.

Congruency and Triangles: • Congruency in triangles: all pairs of corresponding parts (angles and side) are congruent

Different types of congruency:

There are three different ways to determine congruency in triangles (SAS AAS/ASA SSS)

SAS: side-angle-side • The triangles have two pairs of congruent sides and one congruent angle AAS/ ASA: angle-angle-side / angle-side-angle • The triangles have two pairs of congruent angles and one congruent side SSS: side-side-side • The triangles have all three sides congruent

What you need to know to do these problems:

First you need to know all the types of triangle congruency shown above, so you are able to determine if the two triangles are congruent.

Second you will need to be able to determine if a side or angle is congruent by using various different skills, like, the Pythagorean theorem, ratios, and angle relationships, and trigometric functions (SIN, COS, and TAN)

Problems that you will see: Various problems include triangles with missing angles but you are given sides or other angles and you must use the information you are given and previous knowledge about triangles and angles to solve for the missing angle.

Another type of problem is where you must use the Pythagorean theorem to find a missing side length or using SOHCAHTOA to find an angle or side.

Common Mistakes: The most common mistake is naming the type of congruency. For example some people make up their own like SSA or AA because they all sound alike.

Another common mistake made is errors in angle relationships. For example someone might think that two angles are supplementary when they are corresponding and then they find the angle wrong which would then further lead to errors in their final answers.

There are also errors made in trigometric functions. People might use the wrong function to try and find a missing angle.

Lastly there may be some errors in assuming data that is not given, or common errors in Pythagorean theorem or others steps in finding sides.

BY: Maggie, Andrew, and Georgia