Question

order the angles from least to greatest for 9 - 10 then greatest to least for 11 - 12.
9.
10.
11.

1. graph bcd with b(0, 6), c(2, - 5), d(-8, - 1), then order from greatest to least.

Explanation:

9.

Step1: Identify the side - angle relationship

In a triangle, the larger the side length, the larger the angle opposite it.
For \(\triangle NRQ\), the side lengths are \(17m\), \(21m\), and \(24m\).

Step2: Order the angles

The angle opposite the side of length \(17m\) is \(\angle N\), the angle opposite the side of length \(21m\) is \(\angle R\), and the angle opposite the side of length \(24m\) is \(\angle Q\).
Since \(17<21<24\), by the side - angle relationship in a triangle (\(a < b < c\) implies \(\angle A<\angle B <\angle C\) where \(a,b,c\) are side lengths and \(\angle A,\angle B,\angle C\) are the angles opposite to them respectively), we have \(\angle N<\angle R<\angle Q\).

10.

Step1: Identify the side - angle relationship

For \(\triangle GJH\), the side lengths are \(6in\), \(7in\), and \(10in\).
The angle opposite the side of length \(6in\) is \(\angle G\), the angle opposite the side of length \(7in\) is \(\angle H\), and the angle opposite the side of length \(10in\) is \(\angle J\).

Step2: Order the angles

Since \(6 < 7<10\), by the side - angle relationship (\(a < b < c\) implies \(\angle A<\angle B <\angle C\)), we have \(\angle G<\angle H<\angle J\).

11.

Step1: Identify the side - angle relationship

For \(\triangle XYZ\), the side lengths are \(24m\), \(25m\), and \(27m\).
The angle opposite the side of length \(24m\) is \(\angle X\), the angle opposite the side of length \(25m\) is \(\angle Y\), and the angle opposite the side of length \(27m\) is \(\angle Z\).

Step2: Order the angles

Since \(27>25 > 24\), by the side - angle relationship (\(a>b > c\) implies \(\angle A>\angle B>\angle C\)), we have \(\angle Z>\angle Y>\angle X\).

12.

Step1: Calculate the side lengths

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(BC\): \(x_1 = 0,y_1 = 6,x_2 = 2,y_2=-5\), \(BC=\sqrt{(2 - 0)^2+(-5 - 6)^2}=\sqrt{4 + 121}=\sqrt{125}\approx11.18\).
For \(CD\): \(x_1 = 2,y_1=-5,x_2=-8,y_2=-1\), \(CD=\sqrt{(-8 - 2)^2+(-1+5)^2}=\sqrt{100 + 16}=\sqrt{116}\approx10.77\).
For \(BD\): \(x_1 = 0,y_1 = 6,x_2=-8,y_2=-1\), \(BD=\sqrt{(-8 - 0)^2+(-1 - 6)^2}=\sqrt{64 + 49}=\sqrt{113}\approx10.63\).

Step2: Order the angles

Since \(BC>CD>BD\), by the side - angle relationship (\(a>b > c\) implies \(\angle A>\angle B>\angle C\)), the angles opposite these sides ( \(\angle D\) opposite \(BC\), \(\angle B\) opposite \(CD\), \(\angle C\) opposite \(BD\)) are ordered as \(\angle D>\angle B>\angle C\).

Answer:

1. \(\angle N<\angle R<\angle Q\)
2. \(\angle G<\angle H<\angle J\)
3. \(\angle Z>\angle Y>\angle X\)
4. \(\angle D>\angle B>\angle C\)