Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

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Answer 1

1st question:

1. All of the sides are congruent.
2. The diagonals are perpendicular
3. The diagonals bisect opposite angles.

2nd Question:

• m∡HGI=108°

3rd Question:

• y=56.92

Explanation:

The three properties that are true for a square but not for all rectangles:

• All of the sides are congruent.
• This is not true for all rectangles, as a rectangle can have two pairs of equal sides, but the two pairs of sides can be different lengths.
• The diagonals bisect each other at right angles.
• This is not true for all rectangles, as the diagonals of a rectangle can bisect each other at an angle other than 90 degrees.
• The diagonals bisect opposite angles.
• The diagonals of a rectangle do not necessarily bisect opposite angles. However, the diagonals of a square do bisect opposite angles.

All other properties are true for both square and rectangle.

`\hrulefill`

For 2nd Question:

Given:

m∡IEF=36°

EFGH is a isosceles triangle

EFGI is Parallelogram

It means

IG║EF and GF║IE

To find:

m ∡HGI=?

Solution:

m∡IEF=m∡HIG Being the corresponding angle

m∡HIG = 36°

again,

m∡IEF= m∡IGF since the opposite angle of a parallelogram is equal.

m∡IGF = 36°

again,

m∡IEF = m∡GHI

m∡GHI = 36°

Since the triangle of two sides of an isosceles trapezoid are congruent and their respective angle is also congruent.

Now,

In Δ GHI

m∡GHI + m∡HIG + m∡HGi =180°

SInce the sum of the interior angle of the triangle is supplementary.

36°+36°+ m∡HGi =180°

m∡HGi =180°-36°-36°

therefore, m∡HGI=108°

`\hrulefill`

For 3rd Question:

Given:

m∡A=100°

m∡B=13x

m∡C=7x+y

ABCD is a parallelogram.

it means: AD ║ BC and AB║CD

To find.

y=?

Solution:

∡A+∡B =180° Being co interior angle

100°+ 13x=180°

13x=180°-100°

13x=80°

`x=(80)/(13)`

x=6.154

again,

∡A=∡C since the corresponding angle of the parallelogram is equal.

100°=7x+y

100°=7*6.15+y

y=100°-7*6.154

y=56.92

Therefore, the value of y is 56.92