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Sliva [168]
3 years ago
11

Ben uses a compass and a straightedge to bisect angle PQR, as shown below: The figure shows two rays QP and QR with a common end

point Q. An arc drawn from Q cuts the ray QP at A and the ray QR at B. Two small arcs intersect between the lines QP and QR. The point of intersection of the arcs is labeled S. The points Q, S, and T are joined with a line. Which statement best explains why Ben uses the same width to draw arcs from A and B that intersect at S? BQ = BS when ∠AQS ≅ ∠BQS. AQ = AS when ∠AQS ≅ ∠BQS. ∠AQS ≅ ∠BQS when AS = BS and AQ = BQ. ∠AQS ≅ ∠BQS when AS = BQ and BS = AQ.

Mathematics
2 answers:
maria [59]3 years ago
6 0

Answer:

The correct option is;

∠AQS ≅ ∠BQS when AS = BS

Step-by-step explanation:

Given that AQ is equal to BQ. When AS is drawn congruent to BS, we have;

QS is congruent to SQ by reflective property

Therefore;

The three sides of triangle QAS are congruent to the three sides of triangle QBS, from which we have;

∠AQS and ∠BQS are corresponding angles, therefore;

∠AQS ≅∠BQS because corresponding angles of congruent triangles are also congruent.

eimsori [14]3 years ago
4 0

Answer:

∠AQS ≅ ∠BQS when AS = BS and AQ = BQ

Step-by-step explanation:

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2 years ago
This table shows the income and expenses for a school carnival.The schools goal was to raise $1100.By how much did the school ex
algol [13]
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Goal = $1100

Exceeded by = $1129 - $1110 = $9.

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Answer: The school exceed their goal by $9.
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6 0
3 years ago
I need help pls. Question 11
g100num [7]

Answer:

T = .17m + 50

Step-by-step explanation:

T = Total cost

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3 0
3 years ago
3. ms. Johnson placed two different orders with TR's special item store. each order was for 40 jars with the circus logo imprint
denis23 [38]
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3 0
3 years ago
A lighthouse is built on an exposed reef, 4.5 miles off-shore. The shoreline is perfectly straight, and a town is located 6 mile
Alisiya [41]

Answer: 3.94 hours

Step-by-step explanation:

From the question, the following parameters are given:

Distance offshore = 4.5 miles

Distance downshore = 6 miles

Speed when running = 3.4 mph

Speed with boat = 1.8 mph

distance of boat rowing = sqrt(4.5^2 + x^2)

Where

Speed = distance/time

Time = distance/speed

Time = distance of boat rowing/1.8

distance of running = 6 - x

Time = (6-x)/3.4

total travel time

t = sqrt(4.5^2 + x^2)/1.8 + (6 - x)/3.4

dt/dx = x/(1.8×sqrt(4.5^2 + x^2) - 1/3.4

d^2t/dx^2 = +ve at any x

x is at its minimum when dt/dx=0

x/(1.8×sqrt(4.5^2 + x^2) = 1/3.4

x = 6/sqrt(253) × 4.5 = 1.697 miles

Substitute x in

t = sqrt(4.5^2 + x^2)/1.8 + (6 - x)/3.4

We obtaine

t = sqrt(4.5^2 + 1.697^2)/1.8 + (6 - 1.69)/3.4

t = 2.672+ 1.266 = 3.94 hours

7 0
3 years ago
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