MATHEMATICS HIGH SCHOOL

Provide the reasons for the fol owing proof Given: JK ≅ KL, NK ≅ KM
Prove ΔNKJ ≅ ΔMLK

Statements Reasons

1. JK≅KL,NK≅KM 1. Given

2.
3. ΔNKJ ≅ ΔMLK 3.________

ANSWER CHOICES

a. reflexive property of ≅ ; SAS
b. reflexive property of ≅ ; ASA
c. vertical angles are congruent; ASA
d. vertical angles are congruent; SAS

Answers

Answer 1

Answer:

Answer:

Option d is correct.

Vertical angles are congruent;

SAS

Step-by-step explanation:

Given: $JK \cong KL$ , $NK \cong KM$

In ΔNKJ and ΔMLK

$JK \cong KL$ and [Side] {Given}

$NK \cong KM$

Vertical angles states that the two lines intersect to make an X, angles on opposite sides of the X are called vertical angles.

i.e $\angle NKJ$ and $\angle MKL$ are vertical angles.

Also, vertical angles are congruent.

$\angle NKJ \cong \angle MKL$ [Angle] [Vertical angles are congruent]

SAS(Side-Angle-Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

then, by SAS postulates;

$\triangle NKJ \cong \triangle MLK$ Hence proved!

Therefore:

Statement Reason

1. $JK \cong KL$ , $NK \cong KM$ Given

2. $\angle NKJ \cong \angle MKL$ Vertical angles are congruent

3. $\triangle NKJ \cong \triangle MLK$ SAS

Answer 2

Answer: Answer would be D, as the triangles are congruent due to being verticle angles (literally, you can just see theyre the same). Its SAS because you have 2 exact same sides, plus an exact same angle

Related Questions

A student bought a juice pouch for $2.50 and 3 bags of chips . The total cost was $5.05 write and solve an equation to determine the cost of a bag of chips
PLEASE HELP What is the solution to the sentence ''A number decreased by -5 is at least 7''?
What's 2/3 written as a fraction with a denominator of 9?
4x+11<23 solve this equation
Which of the following numbers is closest to 5?OA. √23 OB. √26 OC. √28 OD. √/22

Which temperature during the week is the closest to 0? Explain how you decided this using absolute value.A -3.5 F
B 5 F
C 1.5 F
D -0.5
E -2 F
the rest of the choices 2.5 and -4

Answers

Answer: I would have to go with e because it is the closest because it is -2 and if it were to get to zero it wouldn't take that long.

Step-by-step explanation:

Write an equation of the parabola in vertex form.

Answers

Answer:

$y= -\frac19(x-3)^2+1$

Step-by-step explanation:

the x-3 is to shift a normal parabola 3 to the right

the +1 is to lift the top up by one

the -1/9 is to compress and swapt it around

Answer:

y =- $(1)/(9)$ (x - 3)² + 1

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (3, 1) , thus

y = a(x - 3)² + 1

To find a substitute another point on the graph into the equation

Substitute (1, $(5)/(9)$ ) into the equation

$(5)/(9)$ = a(1 - 3)² + 1 ( subtract 1 from both sides )

- $(4)/(9)$ = 4a ( divide both sides by 4 )

a = - $(1)/(9)$

y = - $(1)/(9)$ (x - 3)² + 1 ← equation of parabola in vertex form

What is the answer to the problem
7 1/5-6 2/3=

Answers

7 18/15-2 10/15=4 8/15

7 1/5 - 6 2/3
Make both fractions have the same denominator
7 3/15 - 6 10/15
Make both mixed numbers into improper fractions
108/15 - 100/15
Subtract the numerator but NOT the denominator
Final Answer: 8/15

Frank swims laps during swim practice. His coach tells him to swim a certain number of meters (total) each week. Here's a formula for this scenario:n=t/p

t= total number of meters
p= length of a lap (in meters)
n= number of laps frank swims

Rewrite the formula to determine the length of a lap

Answers

n = t/p

t = total number of meters
p = length of a lap (in meters)
n = number of laps frank swims

Determine the length of a lap, p.

n = t/p

1) remove p as a denominator by multiplying both side w/ p.
p*n = p(t/p)
pn = t

2) remove n by dividing both sides with n.
pn / n = t/n

*numerator n and denominator n cancels each other out.

p = t/n

Answer:

$p=(t)/(n)$