Question

Triangles XYZ and EGF are shown. Side XY is 3.0 inches and angle YZX is 107 degrees. Side FG is 2.4 inches and side EF is 1.3 inches. Angle GEF is 48 degrees. Given that triangle XYZ is congruent to triangle EGF, find the measurements of the unknown sides and angles. ZX = __ inches. EG = __ inches. m∠X = __ degrees. m∠G = __ degrees.

Answer 1

ZX is 2.4 inches and EG is 3.0 inches. The measure of angle X is 48 degrees, and the measure of angle G is 25 degrees, found by subtracting the known angles from 180 degrees because the sum of angles in a triangle is always 180 degrees.

Step-by-step explanation:

To find the unknown sides and angles of congruent triangles XYZ and EGF, we use the fact that all corresponding sides and angles are equal in congruent triangles. Since triangle XYZ is congruent to triangle EGF, we can deduce the following:

• ZX equals EG
• angle X equals angle G.

We already know that:

• XY = 3.0 inches
• angle YZX = 107 degrees
• FG = 2.4 inches
• EF = 1.3 inches
• angle GEF = 48 degrees.

Using these values, we can determine:

• ZX = FG = 2.4 inches
• EG = XY = 3.0 inches
• m∠X = m∠G = angle GEF = 48 degrees, because congruent triangles have equal corresponding angles.

Finally, to find angle G, we subtract the known angles from 180 degrees (since the sum of angles in a triangle is 180 degrees):

• m∠G = 180 degrees - 107 degrees - 48 degrees
• m∠G = 25 degrees