Explain why having three congruent angles in two triangles is not a good way to prove two

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Draw an equilateral triangle with side lengths of 1. Each angle here is 60 degrees, which is true of any equilateral triangle.

Now draw another equilateral triangle that has side lengths of 2 units. Clearly this triangle is not the same size as the previous one, but the angles are all still 60 degrees.

We have an example in which there are 2 triangles with the same angles, but the triangles are not congruent. Therefore, having info about congruent angles only isn't sufficient to prove triangles to be congruent.

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Ilia_Sergeevich [38]

Only the triangles in figures <u>5 are congruent</u>

<h3>Further explanation </h3>

Triangles are said to be congruent if:

1. all three sides equal (SSS ---> side, side, side)
2. two sides and the included angle of 2 triangles, are equal (SAS -> Side, Angle, Side)
3. If the two angles and the included sides of the 2 triangles are equal (ASA -> Angle, Side, Angle)
4. If the two angles and the non-included sides of 2 triangles are equal (AAS -> Angle, Angle, Side)

1. △ABC ≠ △DCE : not congruent

at least 3 parts (sides or angles) are compared, in the picture only 2 sides are compared

2. △ABC ≠ △XYZ : not congruent

the angles not includes between two sides

3. △RST ≠ △VUT : not congruent

a minimum of 3 parts (sides or angles) are compared, in the picture only 1 angle and 1 side are compared

4. △DEF ≠ △DHG : not congruent

at least 3 parts (sides or angles) are compared, in the picture only 2 sides are compared

5. △JKL ≅ △KJM : congruent with ASA theorem

<h3>Learn more </h3>

Triangles UVW = XYZ might not be congruent

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