Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW
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Answer 1

1) a) BC,CD,BD

2) b) m∠R is the least

3) c)m∠H is the largest

Explanation:

1) ∠C = 180-60-40

= 180-100

∠C = 80

∠B = 60

∠D = 40

⇒∠D < ∠B < ∠C

The side opposite to the smallest angle is the shortest and the side opposite to the largest angle is the longest

⇒BC< CD < BD

2) GR = 11

BR = 8

BG = 7

The angle opposite to the shortest side is the smallest and the angle opposite to the longest angle is the largest

BG is the shortest side

⇒∠R is the least

3) The angle opposite to the shortest side is the smallest and the angle opposite to the longest angle is the largest

IJ is the longestside

⇒∠H is the largest

Answer 2

1st question: a. BC, CD, BD

2nd question: b. m ∡R is the least.

3rd question: c. m∡H is the largest.

Explanation:

For Question 1st:

• The angles of a triangle add up to 180 degrees. So, if angle B is 60 degrees and angle D is 40 degrees, then angle C must be (180-60-40) =80 degrees.
• The longer the side of a triangle, the larger the angle opposite it. So, since angle C is the largest angle, side BD must be the longest side.
• Similarly, since angle D is the smallest angle, side BC must be the shortest side.
• Side CD is the medium size side as opposite angle is also medium.

Therefore, the sides of triangle BCD in order from shortest to longest are BC, CD, and BD.

So, answer is a. BC, CD, BD

`\hrulefill`

For Question 2nd:

In the Δ BGR

GR=11

BR=8

BG=7

Let's check the points:

• a. m ∡ G is the least. It is not true
  because opposite side BR is not the smallest side as it is bigger than BG. Opposite angle to the side BG is m∡R which is the least.
• b. m ∡R is the least. It is true
  because opposite side BC is the smallest side.
• c. m ∡R is the greatest. It is not true.
  Since opposite side BG which is smallest side of the triangle so, m∡R should be the smallest angle,
• d. m ∡G is the greatest. It is not true.
  Since opposite side BR which is medium side of the triangle so, m∡G should be the mid sized angle.

Therefore, answer is b. m ∡R is the least.

`\hrulefill`

For Question 3rd:

largest side=IJ=365ft

medium side = HJ= 245 ft

smallest side= HI =150 ft

Since, The longer the side of a triangle, the larger the angle opposite it.

Let's check the option:

• a. m∡I is the largest. It is not true.
  Since, opposite side to this angle is HJ. which should be medium angle.

• b. m∡H is the smallest. It is not true.
  Since, opposite side to this angle is IJ. which should be largest angle.

• c. m∡H is the largest. It is true.
  Since, opposite side to this angle is IJ which is largest angle.

• d. m∡I is the smallest. It is not true.
  Since, opposite side to this angle is HJ. which should be medium angle.

Therefore, answer is c. m∡H is the largest.