TRIANGLE PROOFS!!

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Home Page Basic Constructions and Unknown Angles Right Triangle Trigonometry

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Let's start off with a list of concepts!

There are 5 triangle congruences:

SAS (SIDE ANGLE SIDE)
AAS (ANGLE ANGLE SIDE)
HL (HYPOTENUSE LEG)
SSS (SIDE SIDE SIDE)
ASA (ANGLE SIDE ANGLE)

There are only 3 non triangle congruences:

ASS (ANGLE SIDE SIDE)
SSA (SIDE SIDE ANGLE)
AAA (ANGLE ANGLE ANGLE)

Way to justify your triangle congruences are:

Vertical angles are congruent
Interior angles in a triangle sum to 180 degrees
Linear pairs from supplementary angles
If 2 parallel lines are cut by a transversal, then alternate interior angle are congruent
If 2 parallel lines are cut by a transversal, then corresponding angles are congruent
In an isosceles triangle, base angles are congruent
Angles in an equalateral triangle sum to 180 degrees
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
The diagonals bisect each other
A midpoint divides a segment into 2 congruent segments
An angle bisector forms 2 congruent angles
Reflexive Property

Remember the key steps into solving these problems

Know all the concepts by heaart
Sketch a figure if none is given
Plan a strategy
Make a statement and reasons chart
Make sure you have a congruency at the end

Practice with these problems (No answer key will be provided because you have to be 100% sure with your answers in order to succeed) (If you ABSOLUTELY NEED AN ANSWER KEY, EMAIL ME AT QUEENPENGCORN@DISNEYPRINCESSES.COM):

What common issues do students have when learning this topic, what strategies/analogies have you learned that could be used to understand this topic better, how does this topic relate to the world outside of school?
Some common issues that students have is that they don't remember how to label the diagram. They might mistakingly use an incorrect reasoning for their statement. Students also tend to doubt their answers, which is one of the biggest ways to get the proof wrong. A good strategy to remember is to always continue labeling as you finish the problem. The more labeling there is, the more chance there is to getting the proof correct. This topic can be used to help people better explain their statements. Most times, people don't give reasoning to a claim they make. With the use of these problems, people are better able to give thorough explanations and reach their goal more easily.

What common issues do students have when learning this topic, what strategies/analogies have you learned that could be used to understand this topic better, how does this topic relate to the world outside of school?

Some common issues that students have is that they don't remember how to label the diagram. They might mistakingly use an incorrect reasoning for their statement. Students also tend to doubt their answers, which is one of the biggest ways to get the proof wrong. A good strategy to remember is to always continue labeling as you finish the problem. The more labeling there is, the more chance there is to getting the proof correct. This topic can be used to help people better explain their statements. Most times, people don't give reasoning to a claim they make. With the use of these problems, people are better able to give thorough explanations and reach their goal more easily.