Congruent Triangle Combination

Answer:

1) ΔABC ≅ ΔDBC by Side-Angle-Side (SAS)

2) ΔABC ≅ ΔCDB by Side-Side-Side (SSS)

3) ΔABC ≅ ΔDBE by Angle-Angle-Side (AAS)

4) m∠Y = 53°

5) y = 3

6) ΔABC ≅ ΔEDC by Side-Angle-Side (SAS)

7) ΔABC ≅ ΔADC by Angle-Angle-Side (AAS)

8) ΔABC ≅ ΔADC by Side-Angle-Side (SSS)

Step-by-step explanation:

1) Side AC ≅ Side BD      [tex]{}[/tex]        given

Side BC ≅ Side BC      [tex]{}[/tex]            reflexive property

∠DBC ≅ ∠ACB                [tex]{}[/tex]        given

Therefore ΔABC ≅ ΔDBC by Side-Angle-Side (SAS)

2) Side AC ≅ Side BD      [tex]{}[/tex]        given

Side DC ≅ Side BA      [tex]{}[/tex]            given

Side BC ≅ Side BC      [tex]{}[/tex]            reflexive property

Therefore, ΔABC ≅ ΔCDB by Side-Side-Side (SSS)

3) ∠BAC ≅ ∠DEB                [tex]{}[/tex]        given

Side BC ≅ Side BD      [tex]{}[/tex]               given

∠ABC ≅ ∠DBE                [tex]{}[/tex]            vertically opposite angles

Therefore, ΔABC ≅ ΔDBE by Angle-Angle-Side (AAS)

4) ΔXYZ ≅ ΔABC                [tex]{}[/tex]        given

m∠A = 44°, and m∠C = 83°

m∠B = 180 - (44 + 83) = 53°                [tex]{}[/tex]   Sum of angles in a triangle

m∠Y = m∠B = 53°                [tex]{}[/tex]   Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

5) Given that Triangle GHK is congruent to Triangle TZK

GH ≅ XT, KG ≅ KT, and HK ≅ ZK by the definition of congruency

Therefore, GH = 4 = XT = 3y - 2

4 = 3y - 2

3y - 2 = 4

3y = 4 + 2 = 6

y = 6/2 = 3

y = 3

6) Side BC ≅ Side EC      [tex]{}[/tex]           given

Side AC ≅ Side DC      [tex]{}[/tex]              given

∠ACB ≅ ∠DCE                [tex]{}[/tex]            vertically opposite angles

Therefore, ΔABC ≅ ΔEDC by Side-Angle-Side (SAS)

7) ∠BAC ≅ ∠DAC                [tex]{}[/tex]        given

∠ADC ≅ ∠ABC                [tex]{}[/tex]            given

Side AC ≅ Side AC      [tex]{}[/tex]               reflexive property

Therefore, ΔABC ≅ ΔADC by Angle-Angle-Side (AAS)

8) Side AD ≅ Side BC      [tex]{}[/tex]           given

Side AC ≅ Side AC      [tex]{}[/tex]               reflexive property

Side AB ≅ Side DC      [tex]{}[/tex]                given that the included angle between the two legs side AD and side AC and side AC and side BC are both acute, the third sides side AB and side DC are equal

Therefore, ΔABC ≅ ΔADC by Side-Angle-Side (SSS)

I NEED HELP . I'm having trouble trying to figure out how to answer this can anyone help please?

3c+5=23 what is c? c=3 c=6 c=7 c=18​

Which of the following numbers is irrational?
0.13
✓3
-0.3

Approximate the value of the square root of 110 to the nearest hundredth

help pls im so confused

Each day Jimmy feeds his horse 2.34 pounds of oats. He also feeds it hay. The weight of the hay is 3.5 time the weight of the oats. What is the combined weight of oats and hay that Jimmy feeds his horse in ONE week?

GCF of 50 and 100 is..

Find the rate of change
(Pls help!)​

What’s the rate of change of y=5.75x-2.5(x-2)

Will give brainiest for the correct answer! please!

7x+5y=40 2x+4y=-4

Solve the system of equations

-66/22 to a decimal PLEASE I NEED THE ANSWER!!! I'LL MARK BRAINLIEST ​

9-9÷9+9-9÷9=??????


25 points


and brainits for the first right answer

The table below shows the total cost for purchasing a certain number of equally-priced concert tickets.
Total cost (in dollars) Number of concert tickets
110110110 222
275275275 555
440440440 888
Write an equation to describe the relationship between ttt, the number of tickets, and ccc, the total cost of tickets.

Use the quadratic formula to solve the equation.
5x2-3x + 1 = 0
X=

The perimeter of the rectangle is 42 inches. Find the value of x.

The temperature in Anchorage, Alaska was -3°C in the afternoon. After the sun went down, the temperature dropped 6 degrees. Write an equation to represent the situation. What was the temperature after the sun went down? ( 3 points )

A scale drawing of a playhouse is shown below. What is the total height of the actual playhouse?

A. 4 ft
B. 6 ft
C. 8 ft
D. 16 ft​

HELP DUE IN 10 MINUTES ​

HELP WILL MARK BRAINLIEST

Help find domain and range

its one in the morning and i cant sleep

As an estimation we are told 5 miles is 8 km.
Convert 42.5 miles to km.

Can someone plz explain I would appreciate it

question in the picture!!

looking for the answer of 3) and 4) !!

<3

Function 1: Alan starts with $30 this week. He spends $5.30 per week. Let y be the amount remaining as a function of the number of weeks, X. 0 30 1 24.70 2 19.40 3 14.1​

HELP PLEASE ASAP


Solve for x in the diagram below

Function A is represented by the equation y = 4x + 6.
Function B is a linear function that goes through the points shown in the
table.
x 1
3 4
ic
y 3 9 12 18
Which statement correctly compares the rates of change of the two
functions?
A. The rate of change of function A is 6.
The rate of change of function B is 3.
B. The rate of change of function A is 4.
The rate of change of function B is 6.
OC. The rate of change of function A is 6.
The rate of change of function B is 6.
D. The rate of change of function A is 4.
The rate of change of function B is 3

A concession stand charges $2.50 for a bag of popcorn. The stand has already sold 30 bags of popcorn. How many more bags x of popcorn must be sold to earn at least $110? Write your answer as an inequality.

4 movie tickets cost $48. At this rate, what is the cost of 8 movie tickets?