Match the given conditions to the number of triangles that can be constructed from them. the lengths of the three sides are 4 centimeters, 2 centimeters, and 7 centimeters. the measures of two angles are 30° and 60° and the length of the included side is 12 inches. the measures of the three angles are 45°, 75°, and 60°. number of triangles given conditions 0 1 infinitely many

See below  

Step-by-step explanation:

No. of ∆s               Conditions                  

      0               Sides 4 cm, 2 cm, 7 cm

      1                ASA = 30°, 12 in, 30 cm

     ∞                Angles 25°, 75°, 60 °

Reasons:

0 — The two shorter sides are not long enough to meet and form a triangle

1 — The two angles and the included side define a single triangle. The two angles define a single point at which their opposite sides will meet.

∞ — The three angles define the shape of the triangle but not its size. You can dilate the triangle to a larger or smaller size and still have the same angles.

step-by-step explanation:

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