Answer:
Step-by-step explanation:
1). In ΔTPW and ΔGHD,
Triangles will be congruent by the properties of congruence,
1). SSS - (Sides - Side - Side) property of congruence
2). SAS - (Side - Angle - Side) property of congruence
3). ASA - (Angle - Side - Angle) property of congruence
2). ΔABE ≅ ΔMNP
∠A ≅ ∠M
∠B ≅ ∠N
∠E ≅ ∠P
Side AB ≅ Side MN
Side AE ≅ Side MP
Side BE ≅ Side NP
Another way to write the congruency statement → ΔAEB ≅ ΔMPN
3). ΔQRY ≅ ΔJLS
∠Q ≅ ∠J
∠R ≅ ∠L
∠Y ≅ ∠S
Side QR ≅ Side JL
Side RY ≅ Side LS
Side QY ≅ Side JS
Anthe way to write the congruency statement → ΔQYR ≅ ΔJSL
B = boys g = girls
.................................
b + g = 195 b = 195 - g
<u>b</u> = <u>8</u>
g 7
Substitute b for 195 - g in the 2nd equation:
<u>b</u> = <u>8</u>
g 7
<u>195 - g</u> = <u>8</u>
g 7
Cross Multiply
8g = 7 . ( 195 - g )
8g = 1365 - 7g
8g + 7g = 1365
15g = 1365
g = <u>1365</u>
15
g = 91
Substitute g for 91 in one of the equations:
b + g = 195
b + 91 = 195
b = 195 - 91
b = 104
S = 104 boys.
x = 3 + y Eqn(1)
y = -2x + 9 Eqn(2)
Let us solve the system of equations with the substitution method
x - 3 = y (Subtracting 3 from both sides of the Eqn(1))
Replacing y = x - 3 in Eqn (2), we have:
x - 3 = -2x + 9
x = -2x + 9 + 3 (Adding 3 to both sides of the equation)
x + 2x = 9 + 3 (Adding 2x to both sides of the equation)
3x = 12 ( Adding like terms)
x = 12/3 (Dividing by 3 on both sides of the equation)
x = 4
Replacing x=4 in Eqn(1), we have:
4 = 3 + y
4 - 3 = y (Subtracting 3 from both sides of the equation)
y=1
The answers are:
x= 4 and y=1
Slope RS: 2/3
Slope ST: -3/2
Slope TU: 4/6 = 2/3
Slope UR: -1/5
Sides RS and TU have the same slope, so they are parallel.
The slope of side ST is the negative reciprocal of the slopes of sides RS and TU, so side ST is perpendicular to sides RS and TU.
Side UR is not parallel or perpendicular to any other side.
The quadrilateral is a trapezoid.
It's called a measuring cup.
