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Dmitriy789 [7]
1 year ago
15

Given that SQ⎯⎯⎯⎯⎯ bisects ∠PSR and PS⎯⎯⎯⎯⎯≅SR⎯⎯⎯⎯⎯, which of the following triangle congruence statements can be used to prove

that ∠P≅∠R?
The figure shows two triangles P S Q and R S Q with a common side S Q.
Mathematics
1 answer:
Novay_Z [31]1 year ago
4 0

The congruency proof that can be used to show that ∠P≅∠R is as given in the steps below.

<h3>How to prove Triangle Congruence?</h3>

From the figure as seen online, we can see that;

The figure shows the same triangles PQS and RQS as in the beginning of the task. Angles SPQ and SRQ are highlighted in red.

Thus, the 2 column proof to show that ∠P≅∠R is;

Statement 1; ∠SPQ≅∠SRQ

Reason 1; Given

Statement 2; SQ bisects ∠PSR

Reason 2; Given

Statement 3; ∠PSQ≅∠QSR

Reason 3; Definition of angle bisector

Statement 4; SQ ≅ SQ

Reason 4; Reflexive Property of Congruence

Statement 5; △PQS≅△RQS

Reason 5; Angle - Angle Side (AAS) Congruency Postulate

Statement 6; PS ≅ SR

Reason 6; CPCTC (Corresponding parts of congruent triangles are congruent)

Read more about Triangle Congruence at; brainly.com/question/7727792

#SPJ1

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The scatter plot shows the amount of sunlight some tomato plants received and the amount of each plant grew
Studentka2010 [4]

Answer:

Option D

Step-by-step explanation:

The complete question is attached herewith.

Also the options for the same are as follows -

What is the meaning of the slope of the trend line shown on the scatterplot?  

A A plant grows about 3 inches for every 2 hours of sunlight it receives.  

B A plant grows about 2 inches for every 3 hours of sunlight it receives.  

C A plant grows about 3 inches for every 1 hour of sunlight it receives.  

D A plant grows about 1 inch for every 3 hours of sunlight it receives.

Solution

If we look at the graph, we can see that in 6 hours the tomato plant grew by 2 inches.

At the X axis, when x = 6 hours, the y co-ordinate at X = 6 hours is 2 inches.

Hence, It can be interpreted that 1 inch of the tomato plant grows in 3 hours.

Hence, option D is correct

3 0
2 years ago
Dan has ¾ of a cake left over from his birthday party. His best friend Amy ate 1/7 of the leftover cake. How much of the cake do
Dafna1 [17]

Answer:

  • 9/14 of cake left

Step-by-step explanation:

<u>3/4 left and 1/7 of that eaten:</u>

  • 3/4 - 3/4(1/7) =
  • (3/4) (1 - 1/7) =
  • (3/4)(6/7) =
  • 18/28 =
  • 9/14

4 0
2 years ago
Read 2 more answers
Find the volume of a cone with a 3 cm diameter and a 5 cm height
Darya [45]

Step-by-step explanation:

Substitute r = 3 and h = 5 into the formula. Volume V=13⋅π⋅9⋅5=15πcm3=47.1cm3.

3 0
2 years ago
The 8th grade is selling tickets to the 8th grade formal.The cost per ticket is $15.The decorations and food cost $600,and each
MArishka [77]

Answer:

Step-by-step explanation:

Each ticket is $15.  The number of tickets is what we are trying to solve for.  The class spends a certain amount of money to prepare for the formal.  They hope that the money they make in ticket sales is MORE than what they spend.  The expression that represents the number of tickets at $15 each is 15x, where x is the number of tickets.  They hope that the sales are greater than what they spend, so what we have so far is

15x >

Greater than what, though?  What do they spend?  They spend 600 for the food, so

15x > 600...

but they also have to print a certain, unknown number of tickets at .50 each.  The expression that represents the printing of each ticket is .5x (we can drop the 0; it doesn't change the answer or make it wrong if we drop it off).  So the cost for this affair is the food + the printing.

15x > 600 + .5x

Solve this inequality for x.  Begin by subtracting .5 from both sides to get

14.5x > 600 so

x > 41.3

Because we are not selling (or printing) .3 of a ticket, it's safe to say (and also correct!) that they need to sell (and print) 41 tickets.  If they sell 41 tickets, the profit is found by

15(41) > 600 + .5(41)

615 > 600

This means that at 41 tickets, they make a profit.  At 40 tickets, the inequality looks like this:

15(40) > 600 + .5(40) and

600 > 620.  This is not true, so 40 tickets isn't enough.

8 0
3 years ago
Simplify 5m-2(6m-5)+2<br><br>a. -7m-8<br>b. -7m+12<br>c. 17m+12<br>d. 17m-8
fgiga [73]

The answer is B. -7m+12.


First distribute the -2 to 6m and -5.

5m-2(6m-5)+2

5m+(-2*6m)+(-2*-5)+2

5m+-12m+10+2


After that, combine the like terms.

5m+-12m+10+2

-5m+-12m=-7m

10+2=12


The simplified expression is -7m+12.

7 0
3 years ago
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