Given that NPQR, MN is congruent to MR and NP is congruent to QR, fill in the reasons below to prove that MPQ is isosceles

All the reasons to prove that triangle MPQ is isosceles are mentioned below in the explanation section.

Step-by-step explanation:

1. NPQR, MN is congruent to MR

Reason: Congruency is defined as , any shape or geometry is become other by application of flips, translations, rotations, movement, angle change or the combination of any then these two shapes are congruent. Here, MR line and MN are one shape just angles are changed.

2. Angle of N ≅ Angle of R

Reason: It is true because the Triangle MNR is a isosceles triangle, having two equal angles and two same sides.

3. Triangle MNP is congruent to Triangle MRQ

Reasons: Because, firstly MN is congruent to MR, Angle of N and Angle of R is same, thirdly, NP is congruent to QR.

4. MP ≅ MQ

Reason: Similar side of congruent triangle MNP and MRQ.

5. Triangle MPQ is isosceles:

Reason: Because MP and MQ are congruent, hence triangle MPQ is isosceles with two equal angles and two equal sides because of congruency of MP and MQ.

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step-by-step explanation:

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answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere