P, Q, R and S are four points on a circle.
PTR and QTS are straight lines.
Triangle PTS is an equilateral triangle.
Prove that triangle PQR and
triangle SRQ are congruent.
S
Note: The reason for any statement has to be written on the same line (eg. angle ABC = angle BDE because...)
Total marks: 4
Answers
Answer:
Triangle PTS is an equilateral triangle because all sides are equal lengths.
Angle TPS and angle TSP are equal because it is an equilateral triangle.
Triangle PQS and triangle SRP are congruent because of the side-angle-side theorem.
Segment PQ is congruent to segment SR because congruent sides of congruent triangles are congruent.
Segment PR is congruent to segment SQ because congruent sides of congruent triangles are congruent.
Triangle PQR and triangle SRQ are congruent because of the side-side-side theorem.
Δ PQR and Δ SRQ are congruent By SSS rule .
What is Congruence in Triangles?If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
What are the conditions of Congruent in Triangles?Two triangles are said to be congruent if they are of the same size and same shape. There are 5 conditions for two triangles to be congruent. They are SSS, SAS, ASA, AAS, and RHS congruence properties.
According to the question
P, Q, R and S are four points on a circle.
PTR and QTS are straight lines.
Triangle PTS is an equilateral triangle.
In ΔPTS ,
∠PTS = ∠TPS = ∠TSP = 60°
PT = PS = ST
In ΔPQS and ΔSRP
PS = SP (common side of triangle )
∠QSP = ∠RPS = 60°
∠PQS = ∠SRP ( Angles between same base and parallels are equal)
Therefore,
ΔPQS ≅ ΔSRP (ASA rule)
PTR = QTS (by CPCT)
PQ = SR (by CPCT)
∠QPS = ∠RSP (by CPCT)
Now , in Δ PQR and Δ SRQ
PQ = SR (proved above )
QR = QR (common side )
PR = QS (proved above )
Therefore, Δ PQR ≅ Δ SRQ (By SSS rule)
Hence, Δ PQR and Δ SRQ are congruent By SSS rule .
To know more about Congruence in Triangles here:
https://brainly.com/question/20521780
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
formula for areas of rectangles= width x height
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height=x+5
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since the 5x's cancel out each other
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The area of rectangle is [tex](x^{2} -25)[/tex] unit square.
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A
Step-by-step explanation:
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Select the correct text in the table.
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2.12 + 4
Select the true statements.
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The numerator includes a coefficient of 3.
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
#7:
Costco marks up the price of a $500.00 couch by 25%
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Answers
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is ya answer
i think
sorry if im wrong
Answer:
468.75
Step-by-step explanation:
First we need to add 25% to 500.00 which is 625.
Next we need to subtract 25% from 625.
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m
Q
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P
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M
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
Step-by-step explanation:
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3x - 8y = 24
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Answer:
I will show you how to solve for x and y.
Step-by-step explanation:
-5x + y = -3
3x - 8y = 24
You can isolate y in the first equation, and substitute that into the second equation.
so to isolate y in -5x + y = -3, you would add 5x to both sides
this gives you y = 5x - 3
Then substitute this y into the equation below.
3x - 8(5x-3) = 24 (this way, the y variable disappears)
then distribute the 8 into the bracket
3x - 40x + 24 = 24
combine the variables
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isolate x by moving the constants to one side
-37x = 0
so x = 0
I am not sure if you want the rest, but here it is.
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answers
Step-by-step explanation:
11.
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plz mark my answer as brainlist plzzzz.
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Answers
Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answers
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Answer:
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Answer:
Step-by-step explanation:
425=25x-10x-250
675=15x
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Answers
Answer:
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