Question

order the angles in each triangle from smallest to largest. 23) a) ∠f,∠g,∠h b) ∠f and ∠g;∠h c) ∠g;∠f and ∠h d) ∠h,∠g,∠f 24) a) ∠f,∠g,∠e b) ∠e,∠f,∠g c) ∠g,∠e,∠f d) ∠e,∠g,∠f 25) a) ∠r,∠s,∠q b) ∠q,∠r,∠s c) ∠q,∠s,∠r d) ∠r and ∠s;∠q 26) a) ∠d,∠c,∠e b) ∠d,∠e,∠c c) ∠e,∠c,∠d d) ∠c,∠e,∠d

Explanation:

Step1: Recall angle - side relationship

In a triangle, the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.

Step2: Analyze triangle in 23

In $\triangle GHF$, side $HF = 15$, side $HG=22$, side $GF = 22$. The shortest side is $HF$. The angle opposite $HF$ is $\angle G$. The other two sides are equal, and the angles opposite them ($\angle F$ and $\angle H$) are equal. So the order of angles from smallest to largest is $\angle G;\angle F$ and $\angle H$.

Step3: Analyze triangle in 24

In $\triangle FGE$, side $FE = 12$, side $FG = 17$, side $GE = 25$. The shortest side is $FE$, and the angle opposite it is $\angle G$. The next - shortest side is $FG$, and the angle opposite it is $\angle E$. The longest side is $GE$, and the angle opposite it is $\angle F$. So the order of angles from smallest to largest is $\angle G,\angle E,\angle F$.

Step4: Analyze triangle in 25

In $\triangle QSR$, side $QS = 8$, side $QR = 12$, side $SR = 13$. The shortest side is $QS$, and the angle opposite it is $\angle R$. The next - shortest side is $QR$, and the angle opposite it is $\angle S$. The longest side is $SR$, and the angle opposite it is $\angle Q$. So the order of angles from smallest to largest is $\angle R,\angle S,\angle Q$.

Step5: Analyze triangle in 26

In $\triangle CDE$, side $CD = 13$, side $CE = 23$, side $DE = 17$. The shortest side is $DE$, and the angle opposite it is $\angle C$. The next - shortest side is $CD$, and the angle opposite it is $\angle E$. The longest side is $CE$, and the angle opposite it is $\angle D$. So the order of angles from smallest to largest is $\angle C,\angle E,\angle D$.

Answer:

1. C
2. C
3. A
4. D