b A bisected angle is divided into two equal angles.
C
c A bisected angle is divided into two equal angles.
D
d Remember that ∠ ABC ≅ ∠ DEF.
A
a m∠ DEF=112^(∘)
B
b m∠ ABG=56^(∘)
C
c m∠ CBG=56^(∘)
D
d m∠ DEG=56^(∘)
Practice makes perfect
a Let's start by making sense of the relevant information. The statement
∠ ABC ≅ ∠ DEF
tells us that the angle between BA and BC is congruent with the angle between ED and EF. This means that these angles are equal in measure. Let's mark these angles in blue.
We are also given m∠ ABC = 112^(∘). Therefore, so is m∠ DEF.
m∠ ABC=112^(∘)=m∠ DEF
b We are told that BG bisects ∠ ABC. This means that ∠ ABC is divided into two equal angles.
∠ ABG ≅ ∠ CBG
Let's mark these angles on our diagram in red.
Since m∠ ABC=112^(∘), and BG cuts this angle in half, we can conclude that m∠ ABG is half of 112^(∘).
m∠ ABG=112^(∘)/2=56^(∘)
c Let's think back to Part B. We found that, because BG is a bisector We also know that ∠ ABG is congruent to ∠ CBG.
d We are told that BG bisects ∠ DEF. Therefore, the angle is divided into two equal angles. Since ∠ ABC is congruent with ∠ DEF, the following must be true.
∠ ABG ≅ ∠ CBG ≅ ∠ DEG ≅ ∠ FEG
Let's mark this in our diagram.
