12 multiple-choice questions, progressively harder.
In triangle ABC, which side is opposite angle B?
Solution
Correct answer: B
The opposite side is the side not touching the angle's vertex.
AC does not touch B, so AC is opposite angle B.
Triangle ABC has angles of 40, 65, and 75 degrees at A, B, and C, respectively. Which side is longest?
Correct answer: D
The largest given angle is at C.
The longest side faces that angle, so it is AB.
An existing triangle ABC has side lengths AB of 8, BC of 13, and CA of 10 units. Which angle is largest?
Correct answer: A
The longest side is BC, with length 13.
Its opposite angle is A, so angle A is largest.
Triangle PQR has angles P, Q, and R measuring 50, 60, and 70 degrees, respectively. Which side is shortest?
Correct answer: C
The smallest angle is P, measuring 50 degrees.
The side opposite P is QR, so QR is shortest.
In an existing triangle KLM, KL and LM each measure 9 units and KM measures 14 units. Which angles are equal?
The equal sides KL and LM meet at L.
Their opposite angles are M and K. The isosceles base-angle theorem makes those angles equal.
In triangle ABC, BC is extended through C to D. Angle ACD is 120 degrees and angle A is 42 degrees. Find angle B.
The exterior angle equals the sum of the remote angles A and B.
Triangle LMN is right at M. Which side is the hypotenuse?
The hypotenuse lies opposite the right angle.
M is the right-angle vertex, so LN is the hypotenuse.
P is outside a line. H is its perpendicular foot, and Q is another point on the line. Which segment is shorter?
Triangle PHQ is right at H.
PQ is its hypotenuse, so
P is outside a line. The perpendicular segment PH has length 5 units, and Q is another point on the line. Which claimed length of PQ is impossible?
PQ is the hypotenuse of right triangle PHQ.
A length of 4 units is too short.
Triangle ABC and triangle XYZ are unrelated. Angle A is larger than angle X. What can you conclude about the opposite lengths BC and YZ?
The side-angle ordering theorem compares parts within one triangle.
An angle comparison between unrelated triangles does not determine their side lengths.
In triangle ABC, angle A is smaller than angle B. Which comparison must hold?
BC is opposite angle A, and AC is opposite angle B.
The smaller angle faces the shorter side, so
An exterior angle of a triangle measures 60 degrees. What is the measure of its adjacent interior angle?
The adjacent interior angle and the exterior angle form a straight angle.
Here the exterior angle is smaller than the adjacent interior angle. The exterior-angle inequality applies to remote interior angles.
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