Which statements about the figure are true? Select two options.
2 answers:
<u>Complete Question</u>
The circle is inscribed in triangle PRT. A circle is inscribed in triangle P R T. Points Q, S, and U of the circle are on the sides of the triangle. Point Q is on side P R, point S is on side R T, and point U is on side P T. The length of R S is 5, the length of P U is 8, and the length of U T is 6. Which statements about the figure are true?
Answer:
(B)TU ≅ TS
(D)The length of line segment PR is 13 units.
Step-by-step explanation:
The diagram of the question is drawn for more understanding,
The theorem applied to this problem is that of tangents. All tangents drawn to a circle from the same point are equal.
Therefore:
|PQ|=|PU|=8 Units
|ST|=|UT| =6 Units
|RS|=|RQ|=5 Units
(b)From the above, TU ≅ TS
(d)Line Segment |PR|=|PQ|+|QR|=8+5=`13 Units
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The length measurement of the third side of the triangular playground whose two sides are 24 ft and 30 ft long should be more than 6 but less than 54.
<h3>What is triangle inequality theorem?</h3>
Triangle inequality theorem of a triangle says that the sum of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
(a+b)>c
(b+c)>a
(c+a)>b
There is a triangular playground. The measurements of two sides of a triangular playground are 24 feet and 30 feet.
Suppose the length of the measurement of the third side of the triangular playground is <em>c</em> meters.
As the two sides are 24 ft and 30 ft long. Thus, by the triangle inequality theorem,
For the sides 24 ft and c ft,
Thus, the length measurement of the third side of the triangular playground whose two sides are 24 ft and 30 ft long should be more than 6 but less than 54.
Learn more about the triangle inequality theorem here;