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 angle measures of a triangle?
$55^\circ, 55^\circ, 70^\circ$
$circ$ yes
triangles with these measurements select
$circ$ no
(b) can these be the side lengths of a triangle?
$34\\ \text{m}, 12\\ \text{m}, 20\\ \text{m}$
$circ$ yes
triangles with these measurements

Explanation:

Step1: Sum the given angles

$55^\circ + 55^\circ + 70^\circ = 180^\circ$

Step2: Check triangle angle sum rule

Since the sum equals $180^\circ$, a triangle is possible. For triangles with only equal angle measures, they are similar but can have different side lengths, so they are not congruent.

Step3: Check triangle inequality for sides

For sides 34 m, 12 m, 20 m: $12 + 20 = 32$, and $32 < 34$. The sum of the two shorter sides is less than the longest side, violating the triangle inequality.

Answer:

(a) Yes; Triangles with these measurements are not all congruent
(b) No