Question

I need help figuring out weather they are congruent or not for each. I have tried multiple times and still have not got no correct answers for them. May I please get help

Answer 1

Triangle NMO has two angles that are congruent to two other angles of triangle PQR. We know that because each pair of congruent angles are indicated in the image using the same symbols:

`\begin{gathered} \hat{O}\equiv\hat{R} \\ \\ \hat{N}\equiv\hat{P} \end{gathered}`

Also, each of those triangles has a side, between those angles, that are congruent to each other:

`ON\equiv RP`

So, these two triangles are congruent by the postulate Angle-Side-Angle. Or just ASA.

For triangles HIG and JKL, we see that they have two pairs of congruent sides:

`\begin{gathered} HI\equiv JL \\ \\ IG\equiv LK \end{gathered}`

And also one pair of congruent angles, between those sides:

`\hat{I}\equiv\hat{L}`

Thus, these triangles are congruent by the postulate Side-Angle-Side. Or just SAS.

For triangles VWU and ZXY, we see that they have two pairs of congruent sides:

`\begin{gathered} VW\equiv ZX \\ \\ WU\equiv XY \end{gathered}`

Although

`\hat{W}\equiv\hat{Z}`

those angles are located, relative to the congruent sides, in different locations in each of the triangles. So, we can not say for sure that the triangles are congruent.

Therefore, these triangles are not necessarily congruent.