Mathematics, 02.11.2020 08:50 shdidiod

Unit4: Congruent Triangles Hw 1: Classifying Triangles Gina Wilson (All things algebra) 2014

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Answer from: cicimarie2018

11. Applying distance formula and finding the sides of DEF, triangle DEF can be classified as an: isosceles triangle.

Applying the definition of equilateral and isosceles triangles, the value of x and the measure of the sides of the given triangles are as follows:

12. x = 6

JK = KL = JL = 83

13. x = 18

QR = RS = QS = 29

14. x = 11

DE = CD = 74

CE = 37

15. x = 23

WY = WX = 95

XY = 108

Recall:

All three sides of an equilateral triangle are the same in length.Two sides of an isosceles triangle are equal in length.Distance formula is given as: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

11. Given the vertices:

D(-2, 3), E(5, 5), F(-4, 10),

Find DE, DF, and EF using $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Length of DE:

$DE = \sqrt{(5 -(-2))^2 + (5 - 3)^2} \\\\DE = \sqrt{(7)^2 + (2)^2} \\\\\mathbf{DE = \sqrt{53}}$

Length of DF:

$DF = \sqrt{(-4 -(-2))^2 + (10 - 3)^2} \\\\DF = \sqrt{(-2)^2 + (7)^2} \\\\\mathbf{DF = \sqrt{53}}$

Length of EF:

$EF = \sqrt{(-4 -5)^2 + (10 - 5)^2} \\\\EF = \sqrt{(-9)^2 + (5)^2} \\\\\mathbf{EF = \sqrt{106}}$

Triangle DEF has two equal sides, therefore, it is an isosceles triangle.

12. Given that triangle JKL is equilateral, all it's side will be equal.

Therefore, JK = JL

Substitute

13x + 5 = 8x + 35

Collect like terms

$13x + 5 = 8x + 35\\\\13x - 8x = -5 + 35\\\\5x = 30\\\\\mathbf{x = 6}$

Plug in the value of x to find the measure of the sides of triangle JKL.

$JK = 13x + 5 = 13(6) + 5\\\\\mathbf{JK = 83}$

$KL = 17x - 19 = 17(6) - 19\\\\\mathbf{KL = 83}$

$JL = 8x + 35 = 8(6) + 35\\\\\mathbf{JL = 83}$

JK = KL = JL = 83

13. Triangle QRS is equilateral, meaning all its side are equal.

$QR = 2x - 7\\\\$ RS = 5x - 61

To find x, set QR equal to RS (equal sides).

2x - 7 = 5x - 61

Collect like terms

$2x - 5x = 7 - 61\\\\-3x = -54\\\\\mathbf{x = 18}$

Plug in the value of x to find the measure of the sides of triangle QRS.

$QR = 2x - 7 = 2(18) - 7\\\\\mathbf{QR = 29}$

QR = RS = QS = 29 (equal sides)

14. Since CDE is isosceles, therefore, CD = DE.

Set CD equal to DE

$9x - 25 = 6x + 8\\\\9x - 6x = 25 + 8\\\\3x = 33\\\\\mathbf{x = 11}$

Plug in the value of x to find the measure of the sides of triangle CDE.

$CD = 9x - 25 = 9(11) - 25\\\\\mathbf{CD = 74}$

DE = CD = 74 (congruent sides)

$CE = 10x - 73 = 10(11) - 73\\\\\mathbf{CE = 37}$

15. We are given that triangle WXY is isosceles, therefore, WX = WY.

Set WX equal to WY

$4x + 3 = 7x - 66\\\\4x - 7x = -3 - 66\\\\-3x = -69\\\\\mathbf{x = 23}$

Plug in the value of x to find the measure of the sides of triangle WXY.

$WX = 4x + 3 = 4(23) + 3\\\\\mathbf{WX = 95}$

WY = WX = 95 (congruent sides).

$XY = 5x - 7 = 5(23) - 7\\\\\mathbf{XY = 108}$

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Answer from: alisharodriguez1

12. x = 6, side = 8313. x = 18, side = 2914. x = 11, sides = 74, 74 and 3715. x = 23, sides = 95, 95 and 108

Step-by-step explanation:

11 is incomplete, can't solve

The triangle is equilateral, so all sides are equal, using one pair to find x:

13x + 5 = 17x - 1917x - 13x = 5 + 194x = 24x = 6

Each side is:

13*6 + 5 = 78 + 5 = 83

13.

Sides are equal as triangle is equilateral

QR = 2x - 7RS = 5x - 61QS = x + 11

Finding x by comparing two sides

2x - 7 = 5x - 615x - 2x = 61 - 73x = 54x = 18

Sides are equal

18 + 11 = 29

14.

Equal sides of isosceles triangle:

CD = DE9x - 25 = 6x + 89x - 6x = 8 + 253x = 33x = 11

Sides are

CD = DE = 9*11 - 25 = 99 - 25 = 74CE = 10*11 - 73 = 110 - 73 = 37

15.

Equal sides of isosceles triangle WXY, WX = WY

WX = 4x + 3WY = 7x - 66XY = 5x - 74x + 3 = 7x - 667x - 4x = 3 + 663x = 69x = 23

Sides are:

WX=WY = 4*23 + 3 = 95XY = 5*23 - 7 = 108

Answer from: Quest

the reporter's right

step-by-step explanation:

1/4 = .25 / 25%

Answer from: Quest

figure c

step-by-step explanation:

hope this .

Wich of these figures represents a line ?

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Unit4: Congruent Triangles Hw 1: Classifying Triangles Gina Wilson (All things algebra) 2014
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