topic 6: triangle inequalities 26. which of the following could represent the side lengths of a triangle? check all that apply. 19, 11, 17 23, 28, 52 34, 9, 25 13, 22, 14 27. which of the following lists the sides of △def in order from shortest to longest? a. $ \overline { d e }, \overline { e f }, \overline { d f } $ b. $ \overline { e f }, \overline { d f }, \overline { d e } $ c. $ \overline { e f }, \overline { d e }, \overline { d f } $ d. $ \overline { d f }, \overline { d e }, \overline { e f } $ 28. in △pqr, pq = 11 feet, qr = 7 feet, and pr = 15 feet. which lists the angles in measures order from smallest to largest? a. $ \angle p, \angle r, \angle q $ b. $ \angle r, \angle q, \angle p $ c. $ \angle p, \angle q, \angle r $ d. $ \angle q, \angle r, \angle p $ 29. given the diagram below, which statement is true? a. wx wy 30. the sides of △fgh are fg = 6x + 7, gh = 8x - 5, and fh = 10x - 11. if the perimeter of △fgh is 87 feet, list the angle measures in order from largest to smallest.

Question

topic 6: triangle inequalities 26. which of the following could represent the side lengths of a triangle? check all that apply. 19, 11, 17 23, 28, 52 34, 9, 25 13, 22, 14 27. which of the following lists the sides of △def in order from shortest to longest? a. $ \overline { d e }, \overline { e f }, \overline { d f } $ b. $ \overline { e f }, \overline { d f }, \overline { d e } $ c. $ \overline { e f }, \overline { d e }, \overline { d f } $ d. $ \overline { d f }, \overline { d e }, \overline { e f } $ 28. in △pqr, pq = 11 feet, qr = 7 feet, and pr = 15 feet. which lists the angles in measures order from smallest to largest? a. $ \angle p, \angle r, \angle q $ b. $ \angle r, \angle q, \angle p $ c. $ \angle p, \angle q, \angle r $ d. $ \angle q, \angle r, \angle p $ 29. given the diagram below, which statement is true? a. wx < wy b. xz < xy c. wy > yz d. xy > wy 30. the sides of △fgh are fg = 6x + 7, gh = 8x - 5, and fh = 10x - 11. if the perimeter of △fgh is 87 feet, list the angle measures in order from largest to smallest.

Accepted Answer

### 26. # Explanation: ## Step1: Triangle inequality theorem For three side - lengths $a$, $b$, and $c$ of a triangle, the following must hold: $a + b>c$, $a + c>b$, and $b + c>a$. ### For $19$, $11$, $17$: $11+17 = 28>19$, $11 + 19=30>17$, $17+19 = 36>11$. ### For $23$, $28$, $52$: $23+28=51<52$. ### For $34$, $9$, $25$: $9 + 25=34$. ### For $13$, $22$, $14$: $13+14 = 27>22$, $13+22=35>14$, $14 + 22=36>13$. # Answer: $19,11,17$ and $13,22,14$ ### 27. # Explanation: ## Step1: Find the measure of $\angle D$ In $\triangle DEF$, using the angle - sum property of a triangle ($\angle D+\angle E+\angle F = 180^{\circ}$). Let $\angle D=x$, then $x + 54^{\circ}+56^{\circ}=180^{\circ}$, so $x=\angle D=180-(54 + 56)=70^{\circ}$. ## Step2: Use the side - angle relationship In a triangle, the side opposite the larger angle is longer. $\angle E = 54^{\circ}$, $\angle F=56^{\circ}$, $\angle D = 70^{\circ}$. The side opposite $\angle E$ is $DF$, the side opposite $\angle F$ is $DE$, and the side opposite $\angle D$ is $EF$. # Answer: $DF,DE,EF$ (Option D) ### 28. # Explanation: ## Step1: Use the side - angle relationship In $\triangle PQR$, $QR = 7$, $PQ=11$, $PR = 15$. The side opposite $\angle P$ is $QR$, the side opposite $\angle Q$ is $PR$, and the side opposite $\angle R$ is $PQ$. # Answer: $\angle Q,\angle R,\angle P$ (Option D) ### 29. # Explanation: ## Step1: Use the side - angle relationship In $\triangle WXY$, $\angle W=55^{\circ}$, $\angle X = 58^{\circ}$, $\angle Y=64^{\circ}$, $\angle Z=61^{\circ}$. For $\triangle WXY$, using the side - angle relationship (side opposite larger angle is longer). In $\triangle WXY$, $\angle W=55^{\circ}$, $\angle X = 58^{\circ}$, $\angle Y = 64^{\circ}$. The side opposite $\angle W$ is $XY$, the side opposite $\angle X$ is $WY$, and the side opposite $\angle Y$ is $WX$. # Answer: $WX\angle G>\angle H$ # Answer: $\angle F,\angle G,\angle H$

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QUESTION IMAGE

Question

Explanation:

26.

Step1: Triangle inequality theorem

For \(19\), \(11\), \(17\):

For \(23\), \(28\), \(52\):

For \(34\), \(9\), \(25\):

For \(13\), \(22\), \(14\):

Step1: Find the measure of \(\angle D\)

Step2: Use the side - angle relationship

Step1: Use the side - angle relationship

Answer:

27.