Question

decide whether it is possible for a triangle to have the three angle measures or three side lengths given.
if it is possible, then decide whether all such triangles are congruent.

(a) can these be the side lengths of a triangle?
50 cm, 60 cm, 20 cm
○ yes
triangles with these measurements select
○ no

(b) can these be the angle measures of a triangle?
116°, 123°, 62°
○ yes
triangles with these measurements

Explanation:

Step1: Check triangle inequality (a)

Verify sum of two shortest sides:
$20 + 50 = 70$
Compare to longest side: $70 > 60$
All other pairs also satisfy the inequality:
$20 + 60 = 80 > 50$, $50 + 60 = 110 > 20$

Step2: Check congruence for (a)

By SSS congruence rule, triangles with identical side lengths are congruent.

Step3: Check angle sum (b)

Calculate total angle measure:
$116^\circ + 123^\circ + 62^\circ = 301^\circ$
Compare to triangle angle sum ($180^\circ$): $301^\circ
eq 180^\circ$

Answer:

(a) Yes; Triangles with these measurements are congruent
(b) No