4.4 Triangle Congruence Using ASA, AAS, and HL

which two postulates of the combinations don't work: In other words all the combinations work accept

Ass- doesn't work at all AAA- just proves the triangles similar

For the proofs

Draw on diagram the three parts that you found congruent

For flow chart proofs

Draw the given on the diagram Write the given in two steps The three arrows are the three parts that prove the triangles congruent

Rememebr to always check back at ... and ...

Given and do the property how they solved the proofs, not how you would have done it if they filled out the left side

What is the hypotenuse? And what do the triangles have to be in order to use HL? And info on the Pythagorean theorem

Hypotenuse is the longest side of the right triangle; the side that doesn't help form the right angle The triangles HAVE TO BE RIGHT TRIANGLES A^2+b^2=c^2 Helps you find the missing side of a right triangle

Hypotenuse leg postulate (HL)

If the hypotenuse and a leg in one right triangle are congruent to the hypotenuse and a leg in another right triangle, then the triangles are congruent. Hypotenuse and leg, not leg and leg The triangles have to be right triangles If you know one hypotenuse and one leg then the triangles are congruent

Angle angle side postulate (AAS)

If two angles and a non-included side in one triangle are congruent to two angles and a non-included side in another triangle, then the triangles are congruent. The side is not included! Don't mix up with ASA which is two angles and the included side, AAS is two angles and a non-included side

Angle side angle postulate

If two angles and the included side in one triangle are congruent to two angles and the included side in another triangle, then the two triangles are congruent. The side has to be between the two angles (sandwiched, included) Difference from SAS is SAS is two sides and an included angle, while ASA is two angles and an included side

Third leg theorem is

Not a thing, it is third angle theorem

For flow chart proofs, what is very common? Plus key tips

Reflexive property with the two triangles sharing a side, which is when you use the reflexive property Highlight what you want of the triangles or draw them separately if the lines are confusing Write the two given steps on separate lines and draw them on the diagram

If you are given two angles are both right angles when you want to say those two angles are congruent say

Right angles are congruent to each other When given a line bisects a line for the proof write the two parts of the line bisected are congruent to each other

Before we learned

SSS and SAS Now we learned ASA AAS HL

Be careful; don't mess up ASA and AAS

The difference is ASA is two angles and an included side and AAS is two angles and a non-included side

For the proofs

There are multiple ways to do it and the best way to get better at them is to practice! You need to state three things that are congruent before we say the triangles are congruent Be thorough

When your are seeing if there is enough info to prove tirangles congruent using... their main trick is

They put AAA and ASS, which don't work! Try to memorize the postulates and elimination Comparing two triangles Don't forget about HL

We learned

Three new postulates

All these postulates use

Three parts to prove the triangles congruent (3.3/3.4) 3.2 uses six parts

Reflexive is very common with For normal proofs

Triangles sharing sides The given is already drawn in diagram, while flow chart you have to draw it If shared angle then you have to write three letters

Can't use hl Reflexive property works for ... too

Unless it is given that the triangles are right angles; you can't assume Triangle vs. angle symbol Reflexive property works for angles too

Remember when you are stating triangles, angles, or sides are congruent

You have to write them in order