Name the following segment or point.
given l, m,n are midpoints

median to bc

1. segment am
2. segment bl
3. segment as

1. Segment AM.

Step-by-step explanation:

We have been given a triangle ABC. Points L, M and N re midpoints of the triangle. We are asked to find the median of segment BC.

We know that median of a triangle is line segment connecting the midpoint of a segment to the opposite vertex.

We can see that angle A is the opposite angle to side BC and M is the midpoint of side BC, therefore, segment AM is the median to side BC and 1st option is the correct choice.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)