Triangles, Congruence, and Similarity
Review triangle classification, congruence criteria, and similarity rules from this geometry lesson.
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Questions Covered in This Set
10 cards to master
What is a scalene triangle?
A triangle with all three sides of different lengths.
State the Isosceles Triangle Theorem.
If two sides of a triangle are equal, the angles opposite those sides are also equal (and the converse holds).
What do the angles of any triangle sum to, and what does the Exterior Angle Theorem say?
Angles sum to 180°; an exterior angle equals the sum of the two remote interior angles.
State the Triangle Inequality. Can sides 3, 4, 8 form a triangle?
Any two sides must sum to more than the third. No — 3 + 4 = 7 < 8, so it's impossible.
List the five triangle congruence criteria.
SSS, SAS, ASA, AAS, and HL (right triangles only).
Why are SSA and AAA not congruence criteria?
SSA (the 'donkey' case) can fit two different triangles; AAA only guarantees similarity, not equal size.
What does CPCTC stand for and when is it used?
Corresponding Parts of Congruent Triangles are Congruent — used after proving congruence to conclude remaining sides/angles are equal.
List the three similarity criteria.
AA (two pairs of equal angles), SSS~ (all side ratios equal), SAS~ (two side ratios equal with included angles equal).
If the scale factor between similar figures is k, how do perimeter, area, and volume scale?
Perimeter by k, area by k², volume by k³ — so tripling sides gives 9× the area.
A 6-ft person casts a 4-ft shadow while a flagpole casts a 26-ft shadow. How tall is the pole?
By AA similarity, h/26 = 6/4, so h = 39 ft.
