Question

!25 POINTS! (2 SIMPLE GEOMETRY QUESTIONS)


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Answer 1

1) AC > BC > AB

2) Angle C < Angle A < Angle B

Explanation:

Question 1

From observation of triangle ABC, the measures of the interior angles are:

• m∠A = 60°
• m∠B = 87°
• m∠C = 33°

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

Side BC is opposite angle A.

Side AC is opposite angle B.

Side AB is opposite angle C.

Angle B is the largest angle. As the longest side is opposite the largest angle, the longest side is AC.

Angle C is the smallest angle. As the shortest side is opposite the smallest angle, the shortest side is AB.

So the side lengths of triangle ABC from the greatest to the least are:

• AC > BC > AB

`\hrulefill`

Question 2

From observation of triangle ABC, the sides lengths are:

• AB = 3 cm
• BC = 5 cm
• AC = 6 cm

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

Angle A is opposite side BC.

Angle B is opposite side AC.

Angle C is opposite side AB.

Side AC is the longest side. As the largest angle is opposite the longest side, the largest angle is angle B.

Side AB is the shortest side. As the smallest angle is opposite the shortest side, the smallest angle is angle C.

Therefore, the largest angle is opposite side AC, and the smallest angle is opposite side AB. So the angles of triangle ABC from the least to the greatest are:

• Angle C < Angle A < Angle B

Answer 2

For 1st Question:

`\tt Blank\:1=\boxed{\tt AC}\\\tt Blank\:2=\boxed{\tt BC}\\\tt Blank\:3=\boxed{\tt AB}`

For 2nd Question:

`\tt Blank\:1=\boxed{\tt angle \: B}\\\tt Blank\:2=\boxed{\tt angle\: A}\\\tt Blank\:3=\boxed{\tt angle\: C}`

Explanation:

Note:

Opposite side of largest angle = Largest side

Opposite side of mid-sized angle = mid-sized side

Opposite side of smallest angle = smallest side

For First Question:

In Δ ABC

m ∡B=87° Largest angle

m ∡A = 60° Mid-sized angle

m ∡C=33°m Smallest angle

Since degree of the angle determine the respective side So,

Opposite to the angle m ∡B= side AC

Opposite to the angle m ∡A = side BC

Opposite to the angle m ∡C = side AB

Therefore,

Largest Side = AC

Mid-sized side= BC

Smallest side= AB

Therefore, AC>BC>AB

`\hrulefill`

For Second Question:

In Δ ABC

AC=6 cm Largest Side

BC= 5 cm Mid-sized side

AB=3 cm smallest side

Since length side determine the respective angle. So,

Opposite to the side AC =m ∡B

Opposite to the side BC=m ∡A

Opposite to the side AB=m ∡C

Therefore,

Largest angle =m ∡B

Mid-sized angle =m ∡A

Small sized angle = m ∡C

Therefore, angle B > angle A > angle C