Question

out of these choices, which angle measure is the greatest? a.) m∠a b.) m∠b d.) m∠d f.) m∠f which reason proves the two triangles are congruent? a.) sss d.) sas b.) ssa e.) asa c.) aas f.) hl g) not enough information

Explanation:

Step1: Analyze congruence of first two triangles

In the first two - given triangles, we see two pairs of corresponding sides are marked as equal. Also, the included angles between these sides are given. So, we use the Side - Angle - Side (SAS) congruence criterion.

Step2: Analyze angles in triangles

For the triangle on the left with $\angle A = 40^{\circ}$, since it is an isosceles triangle (two equal - sides), $\angle B=\angle C$. Using the angle - sum property of a triangle ($\angle A+\angle B+\angle C = 180^{\circ}$), we have $40^{\circ}+2\angle B = 180^{\circ}$, so $\angle B=\angle C=\frac{180 - 40}{2}=70^{\circ}$. For the triangle on the right with $\angle E = 50^{\circ}$, since it is an isosceles triangle, $\angle D=\angle F$. Using the angle - sum property ($\angle D+\angle E+\angle F = 180^{\circ}$), we have $2\angle D+50^{\circ}=180^{\circ}$, so $\angle D=\angle F=\frac{180 - 50}{2}=65^{\circ}$.

Answer:

1. D. SAS
2. B. $m\angle B$