Unit 5
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General proofs
HL, SAS, AAS, ASA, SSS
Isoceles theorems
• If the triangle had 2 congruent sides it is isoceles • If the triangle had 2 congruent sides the opposite angles are congruent • If the triangle had 2 congruent angles the opposite sides are congruent
Tip for overlapping triangles
Redraw each one to find corresponding points
How to find shortest/longest side of triangle
Across shortest/longest angle
Double triangle proofs
Highlight both triangles and redraw- also you usually want to use general proofs
REMINDER
REMEMBER TO TRY GENERAL PROOFS TO SEE IF THEY FIT AS WELL AS THE ISOCELES THEOREMS (THESE ARE NOT ALWAYS NECCESSARY)
If the proof has a right angle and you find the hypotenuse
USE HL
Right angle
90 degrees total
Acute triangle
Angles less than 90 degrees
Obtuse angle
Vertex angle is the largest (like in review question), one angle more than 90 degrees but less than 180 degrees
TRIANGLE ANGLE SUM THEOREM
IN ANY TRIANGLE THE SUM OF THE MEASURES OF THE THREE INTERIOR ANGLES IS 180 DEGREES
EXTERIOR ANGLE THEOREM
THE MEASURE OF AN EXTERIOR ANGLE OF A TRIANGLE IS EQUAL TO THE SUM OF THE REMOTE TWO INTERIOR ANGLES
Algebraic finding measures of triangles
Exterior angle theorem & triangle angle sum theorem
If 3 sides of one triangle are congruent to three sides of another triangle, the triangles are congruent
SSS
If 2 sides and the INCLUDED ANGLE of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent
SAS
If 2 angles and the INCLUDED side of one triangle are congruent to the corresponding parts of another triangle the triangles are congruent
ASA
If 2 angles and the NON INCLUDED SIDE OF ONE TRIANGLE ARE CONGRUENT TO THE CORRESPONDING PARTS OF ANOTHER TRIANGLE THE TRIANGLES ARE CONGRUENT
AAS
If the hypotenuse and leg of one right triangle (Look for evidence in given) are congruent to the corresponding parts of another right triangle, the right triangles are congruent
HL
Congruent triangles
Use SSS SAS ASA HL AAS
Tips
-highlight triangles -write proofs theorems, review of the triangles, exterior sum theorem and triangle sum theorem - Stay nervous
Overlapping triangles
When trying to prove overlapping triangles are congruent, look for a side or angle that is SHARED by the triangles (hence why they are overlapping- they share something)