Strategy #16 Know important triangle facts, in addition to what’s in the reference table.

• Equilateral triangles: all angles measure 60° (or π/3 radians) and all sides have the same length.
• Isosceles triangles: two sides are the same length. Base angles are congruent. The altitude bisects the vertex and the base.
• The longest side of a triangle is opposite its largest angle; the shortest side is opposite the smallest angle.
• The sum of two sides of a triangle must be greater than the third side. The difference of two sides of a triangle must be smaller than the third side.
• 30°-60°-90° triangles have side-length ratios of 1:2:\(\sqrt{3}\), and 45°-45°-90° triangles have side-length ratios of 1:1:\(\sqrt{2}\). These facts are extremely important to know because they occur frequently. They are found on the tests reference page, but it’s better to have them memorized.
• cos x = sin (90° - x) where x is one of the two acute angles of a right triangle, and (90° - x) is the other acute angle. This is called the co-function identity. Using it will save time. The identity is a result of the bullet below.
• The two acute angles of a right triangle are complementary.
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Example 1 (practice test 6)
Calculator ok

The two labeled angles are complements of each other (32°+58°=90°). And since the two acute angles of a right triangle must be complementary,  \(\angle A\cong \angle E \), and since, BC/AB = sin 32°, DF/EF = sin 32° as well.