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Sunny_sXe [5.5K]
1 year ago
5

For each shape, write an algebraic expression for its perimeter - part A and B

Mathematics
1 answer:
nikitadnepr [17]1 year ago
5 0

Answer:

a)  p + q + r

b)  2(a + b)

Step-by-step explanation:

The perimeter of a two-dimensional shape is the <u>distance</u> all the way around the outside.

An algebraic expression contains one or more numbers, variables, and arithmetic operations.

A variable is a symbol (usually a letter) that represents an unknown numerical value in an equation or expression.

<u>Question (a)</u>

The length of each side of the triangle is labeled p, q and r.  Therefore, the perimeter is the sum of the sides:

Perimeter = p + q + r

So the algebraic expression for the perimeter of the triangle is:

p + q + r

<u>Question (b)</u>

Not all of the sides of the shape have been labeled.  

However, note that the horizontal length labeled "a" is equal to the sum of "c" and the horizontal length with no label.

Similarly, note that the vertical length labeled "b" is equal to the sum of "d" and the vertical length with no label.

Therefore, the perimeter is twice the sum of a and b:

Perimeter = 2(a + b)

So the algebraic expression for the perimeter of the shape is:

2(a + b)

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Step-by-step explanation:

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Leno4ka [110]

<u>Let's consider the facts at hand</u>:

  • By Vertical Angle Theorem ⇒ ∠BCE = ∠DCF
  • ∠BEC = ∠DFC
  • Sides BE = DF

<u>Based on the diagram, triangles BCE and triangles DCF are similar</u>

   ⇒ based on the Angle-Angle theorem

      ⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC

         ⇒ the two triangles are similar

Hope that helps!

<em>Definitions of Theorem I used:</em>

  • <u><em>Vertical Angle Theorem: </em></u><em>opposite angles of two intersecting lines must be equal</em>
  • <u><em>Angle-Angle Theorem:</em></u><em> if two angles of both triangles are equal, then the given triangles must be similar</em>

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2 years ago
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Answer:

EF = HG and EF || HG

Step-by-step explanation:

A quadrilateral is a polygon shape with four sides and four angles.

A parallelogram is a quadrilateral with two pairs of parallel sides. The following are properties of a parallelogram:

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  2. Opposite angles are equal to each other.
  3. Consecutive angles are supplementary
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If Quadrilateral EFGH with diagonals EG and HF is a parallelogram then EF = HG and EF || HG

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Answer:


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The awnser to this problem is +19.20 because since 24 is bigger than 1.25 it goes on the inside of the house and 1.25 goes on the outside because its smaller.

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