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To find the length of PR, you can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, PR must be less than the sum of PQ and QR, so PR < 20 + 22 = 42. Therefore, PR could be any value less than 42.
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P q plus r pq pr?
p(q + r) = pq + pr is an example of the distributive property.
What is the similarity postulate or theorem that applies.David drew PQR and STU so that P S PR 12 SU 3 PQ 20 and ST 5. Are PQR and STU similar?
Similar SAS-apex
Which concept can be used to prove that the diagonals of a parallelogram bisect each other?
Congruent triangles: Take a parallelogram PQRS. Draw in the diagonals PR and QS. Let the point where the diagonals meet be M, Consider one pair of the parallel sides, PS and QR, say. Consider angles PSQ and RQS: As PS and QR are parallel they are equal (Z- or alternate angles). Now consider angles SPR and QRP: As PS and QR are parallel they are equal (z- or alternate angles). As PS and QR are opposite sides of a parallelogram they are equal in length; thus the triangles PMS and RMQ are congruent (Angle-Angle-Side). As the two triangle are congruent, equivalent sides are equal in length. Thus QM is the same length as MS and PM is the same length as MR As QM is the same length as MS and QMS lie on a straight line, M must be the mid point of QS, ie the diagonal PQ bisects the diagonal QS Similarly PM is the same length as MR and PMR lie on a straight line, thus M must be the mid point of PR, ie the diagonal QS bisects the diagonal PR Therefore the diagonals of a parallelogram bisect each other.
What is the probability of obtaining 4 ones in a row when rolling a fair six sided die?
The following is the probability of obtaining 4 ones IN THE FIRST FOUR rolls of a fair die. Pr(4 1's) = Pr(1)*Pr(1)*Pr(1)*Pr(1) since the events are independent. Pr(4 1's) = Pr(1)4 = (1/6)4 = 1/1296 = 0.000772
In triangle pqr qx perpendicular pr and py perpendicular qr. if pq10cm qr8cm and pr5.6cm find the length of py where qx 7.2cm?
There is a problem with your question: If pq = 10 cm, qr = 8 cm and pr = 5.6 cm then if qx is perpendicular to pr through q it does NOT equal 7.2 cm; it is approx 8.0 cm: Let X be the distance px, then xr = 5.6 - X Using Pythagoras: In pxq: 10² = qx² + X² → qx² = 10² - X² In rxq: 8² = qx² + (5.6 - X)² → qx² = 8² - (5.6 - X)² → 10² - X² = 8² - (5.6 - X)² → 10² - X² = 8² - 5.6² + 2×5.6×X - X² → 2×5.6×X = 10² - 8² + 5.6² → X = (10² - 8² + 5.6²)/(2×5.6) → qx² = 10² - ( (10² - 8² + 5.6²)/(2×5.6) )² → qx = √(10² - ( (10² - 8² + 5.6²)/(2×5.6) )²) ≈ 7.989265 cm ≈ 8.0 cm Similarly, for py: py = √(10² - ( (10² - 5.6² + 8²)/(2×8) )²) ≈ 5.59248 cm ≈ 5.6 cm The obtuse triangle has angles: qpr ≈ 53°, prq ≈ 93°, rqp ≈ 34°; the perpendiculars qx and py lie outside the triangle; angle prq ≈ 93° which is not far off a right angle making sides pr and qr approximately perpendicular, and shows that the perpendiculars to the sides next to it (ie the perpendiculars to pr and qr) will be approximately equal to the lengths of the other side (next to it, ie length of perpendicular to pr will be approx qr, and the length of the perpendicular to qr will be approx pr).
