Unit 3 · Core unit
When two triangles are the same, and when they are the same shape at a different scale. The criteria are the unit, and knowing which do not work matters as much as which do.
What a strong answer looks like
A strong answer names the congruence or similarity criterion by its letters and confirms the parts are in the right order.
Know
SSS, SAS, ASA, AAS, and HL establish congruence. SSA generally does not, because two different triangles can satisfy it.
Apply
List the corresponding parts in order, then name the criterion they match.
Watch out
Claiming congruence from SSA, which is the deliberate trap in this unit.
Study move
Decide congruence for four pairs and name the criterion or explain its absence.
Know
Similar triangles have congruent angles and proportional sides, so one scale factor relates every pair of corresponding lengths.
Apply
Set up a proportion between corresponding sides and solve.
Watch out
Pairing sides that are not corresponding, which produces a plausible wrong answer.
Study move
Find a missing length using a similarity proportion and state the scale factor.
Know
The Pythagorean theorem, its converse, and the altitude-to-hypotenuse relationships connect side lengths without trigonometry.
Apply
Use the altitude relationship when a right triangle is split by an altitude to the hypotenuse.
Watch out
Applying the Pythagorean theorem to a triangle not known to be right.
Study move
Find the altitude to the hypotenuse given the two segments it creates.
Modeling drill
In a right triangle, an altitude to the hypotenuse splits it into segments of 4 and 9. Find the altitude and justify the relationship used.
