Geometry — Lines, Angles, Triangles

Properties of triangles, congruence and similarity.

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Q1 · Geometry — Lines, Angles, Triangles · EASY
In a triangle ABC, angle A = 50 degrees and angle B = 60 degrees. What is the measure of angle C?
Q2 · Geometry — Lines, Angles, Triangles · MEDIUM
Two triangles ABC and PQR are such that AB = PQ, BC = QR, and angle B = angle Q. By which congruence criterion are these triangles congruent?
Q3 · Geometry — Lines, Angles, Triangles · MEDIUM
In triangle PQR, PQ = 6 cm, QR = 8 cm, and PR = 10 cm. In triangle XYZ, XY = 9 cm, YZ = 12 cm, and XZ = 15 cm. Are these triangles similar? If yes, what is the ratio of corresponding sides?
Q4 · Geometry — Lines, Angles, Triangles · HARD
In triangle ABC, D is a point on AB such that AD = 4 cm and DB = 8 cm. A line through D parallel to BC meets AC at E. If AE = 3 cm, what is the length of EC?
Q5 · Geometry — Lines, Angles, Triangles · EASY
Two angles of a triangle are 45° and 65°. What is the measure of the third angle?