What additional information is needed to prove that the triangles are similar? To prove △XYZ ~ △MNO using SSS, you need to know that . Now that you know the length of XZ, you need to know that angle O is congruent to to prove △XYZ ~ △MNO using SAS.

To prove two triangles congruent using SSS rule we need to know all the three sides of triangle that are XY, YZ and XZ of XYZ and also all the three sides of triangle MNO that are MN, NO and MO.

To prove two triangles congruent using SAS rule we need to know the two sides and the angle formed between these two lines of both the triangles.

If XY and YZ sides are known then for SAS rule angle ∠XYZ must be known for using SAS rule.

MrRoyal MrRoyal · Answer 2 · 2021-10-25T18:04:20+02:00

Similar triangles may or may not be congruent.

For [tex]\mathbf{\triangle XYZ \sim \triangle MNO}[/tex] by SSS to be true, all corresponding sides of the two triangles must be congruent
For [tex]\mathbf{\triangle XYZ \sim \triangle MNO}[/tex] by SAS to be true, wo corresponding sides and the angle between these two sides must be congruent

From the question, we have:

[tex]\mathbf{\triangle XYZ \sim \triangle MNO}[/tex] by SSS

The above means that:

Triangle XYZ and triangle MNO are congruent by SSS postulate

So, the following must be true

XY congruent to MN
YZ congruent to NO
XZ congruent to MO

So, for [tex]\mathbf{\triangle XYZ \sim \triangle MNO}[/tex] by SSS to be true, all corresponding sides of the two triangles must be congruent

Similarly, for SAS postulate,

Two corresponding sides and the angle between these two sides must be congruent

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