Question

write an equality relating the given side lengths. If there is not enough informations to reach a conclusion, write no conclusion

Answer 1

1)
`ST > MN`

2)
`BA > BC`

3)
`CF > CD`

4)
`JL > MO`

Explanation:

Let's assume that we have the following four cases in the figure attached.

In order to create inequalities related to the possible angles between the two triangles for each case we ned to use the following theorem:

Hinge theorem""If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle"

Part 1

For this case we have that the angle
`<MLN = 57` and from the graph we know that the angle
`< SRT=90` so then we have that angle
`SRT> MLN` so then we can conclude from the theorem above that:

`ST > MN`

Part 2

For this case we have that the angle
`<BDC = 87` and from the graph we know that the angle
`< BDA=180-87=93` so then we have that angle
`BDA> BDC` so then we can conclude from the theorem above that:

`BA > BC`

Part 3

For this case we have that the angle
`<DEC= 77` and from the graph we know that the angle
`< CEF=180-77=103` so then we have that angle
`CEF> ECD` so then we can conclude from the theorem above that:

`CF > CD`

Part 4

For this case we have that the angle
`<JKL = 60` and from the graph we know that the angle
`< MNO=44` so then we have that angle
`JKL> MNO` so then we can conclude from the theorem above that:

`JL > MO`