Congruence and Proofs
Name the triangle congruence theorem abbreviated by three letters that requires three pairs of equal sides.
SSS
What does the Triangle Angle Sum Theorem tell us about the angles in a triangle?
Their sum is 180 degrees.
What is the mnemonic that we use to remember the Sine, Cosine, and Tangent relationships?
SOH CAH TOA
Use a trig ratio to solve for the missing side: In a right triangle, your focus angle = 30°, hypotenuse = 10. Find opposite side.
5
State the Law of Sines formula
sinA/a = sinB/b = sinC/c
Name the triangle congruence theorem abbreviated by three letters that requires two pairs of equal sides and the included angle.
SAS
What does the Exterior Angle Theorem tell us in terms of the remote interior angles?
The exterior angle is equal to the sum of the remote interior angles.
Describe how to identify the side opposite a focus angle, the side adjacent to a focus angle, and the hypotenuse of a right triangle.
Opposite = across from (not touching) the focus angle.
Adjacent = next to (touching) the focus angle and the right angle.
Hypotenuse = across from (not touching) the right angle.
An observer sights the top of a tower at an angle of elevation 25°. If the observer is 50 m from the tower base, find the tower height (round to the nearest tenth)
23.3
State one of the Law of Cosines formulas.
a2=b2+c2-2bc*cosA
Name the TWO triangle congruence theorems abbreviated by three letters that require two angles and one pair of equal sides.
AAS and ASA
A triangle has angles 35° and 65°. Find the third angle.
80 degrees
Define sine, cosine, and tangent as ratios in a right triangle (opposite, adjacent, hypotenuse)
From a cliff 80 m high, the angle of depression to a boat is 18°. How far horizontally is the boat from the cliff base (round to the nearest tenth)
246.2
What are the three steps we followed when solving Law of Sines and Law of Cosine problems?
1) Label the triangle
2) Plug into the formula
3) Cross Multiply
Identify the triangle congruence theorem abbreviated by two letters that is valid only for Right Triangles.
HL
In isosceles triangle ABC, angle A = 50°, angle B = 80°. If side a (opposite A) = 8, what is the measure of side c (opposite C)?
8
In Trigonometry, we use Sine, Cosine, and Tangent to find missing sides of a Right Triangle. What Trig concept do we use to find missing angles of a Right Triangle?
Inverse Sine, Inverse Cosine, and Inverse Tangent
Solve for the acute angle x:
tan x = 7/24. Give x to the nearest tenth of a degree.
16.3 degrees
Use the Law of Sines to find an angle: In triangle ABC, a = 14, A = 30°, b = 10. Find angle B (round to nearest tenth)
20.9 degrees
What does CPCTC stand for and what does that mean?
In triangle ABC, side BC is extended to point D. If angle A = 42° and angle B = 67°, find the measure of exterior angle ∠ACD and explain your reasoning in one sentence.
109 degrees
Given a right triangle with legs 6 and 8, and hypotenuse 10, find sin, cos, and tan of the angle opposite the leg of length 6 (give answers as fractions)
sin = 3/5
cos = 4/5
tan = 3/4
A student lets out 100 feet of string on a kite from a hand height of 3 feet. The angle between horizontal hand height and the kite is 25º. Find the height of the kite above the ground, to the nearest tenth.
45.3
Use the Law of Cosines to find a side: In triangle ABC, A = 70°, b = 9, c = 12. Find side a (round to one decimal).
12.3