Question

Given the information marked on the diagrams

below, which pair of triangles can not always be
proven congruent?
1)
2)
A
AABC and ADBC
E
H.
AEFG and AHIG
K
D
M
AKLJ and AMJL
M
R
ANOP and ARSP

Answer 1

Given the information marked on the diagrams above, a pair of triangles that can not always be proven congruent is: 4. ΔNOP and ΔRSP.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that triangle ABC and triangle DBC are both congruent triangles:

ΔABC ≅ ΔDBC

Based on the angle, angle, side (AAS) similarity theorem, we can logically deduce that triangle EFG and triangle HIG are both congruent triangles:

ΔEFG ≅ ΔHIG

Based on the side, side, side (SSS) similarity theorem, we can logically deduce that triangle KLJ and triangle MJL are both congruent triangles:

ΔKLJ ≅ ΔMJL

Triangles NOP and RSP cannot always be proven congruent because follows a side-side-angle similarity pattern, which is not one of the triangle congruence postulates.