Question

Prove whether True or False: Two triangles which have 5 of 6 parts (angles and sides) equal must be congruent. Please help me :(

Answer 1

In order for the two to be congruent, one of the following must be equal between the two triangles.

1. SSS (side-side-side)

2. SAS (side-angle-side)
3. ASA (angle-side-angle)

4. AAS (angle-angle-side)

Answer 2

The triangles have all angles and 2 sides

or

all sides and 2 angles

this is enough for the 4 basic congurency tests

Side Side Side test ( needs 3 sides)

Side Angle Side 2 sides and the included angle

Angle Angle Side 2 sides and an angle

Right Hypotenuse Side (only for right angled triangles)

Answer 3

But since there is no mention about these parts being corresponding does that mean it's not possible?

Answer 4

its true!!!

Answer 5

But how is it true if the angles and sides don't correspond?

Answer 6

look at it this way:
we either have that 3 sides are the same and 2 angles the same
or 2 sides the same and 3 angles the same

if the three sides are the same the triangles are congruent by SSS

if two sides are the same and all three angles are the same then we have congruence by SAS, since whichever angle we pick will be congruent to the other

Answer 7

Oh wow. Yeah, when you put it like that it seems like a no brainer. Thank you so much!

Answer 8

welcome :)