What is the length of mn?

58 cm
75 cm
88 cm
116 cm

The length of MN is 58 cm.

Step-by-step explanation:

In the given figure we can see that  AM = MB

So, M is the mid point of AB.

Also, BN = NC ( Consider the given figure )

So, N is the mid point of BC.

Since M and N are the midpoints of AB and BC .

So, by mid segment theorem which sates that the segment joining the midpoints of any two sides of a triangle will be parallel to the third side of the triangle and half its length.

⇒ MN is parallel to AC

and  

Thus , the length of MN is 58 cm.

The length of MN is 58 cm.

Step-by-step explanation:

Given the figure in which

AM=MB, CN=NB

So, M and N are the mid point of AB and BC

∴ By mid point theorem which states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side of the triangle and half the length of third side.

⇒ MN is parallel to AC and also half of third side i.e AC

Hence, the length of MN is 58 cm.

Thus , the length of MN is 58 cm.

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.