Dorsain, this is the solution for option A:
Option A:
Step 1: Let's calculate the distance from A to B, as follows:
d = √0² - -5² + 0² - -7²
d = √5² + 7²
d = √25 + 49
d = √74
d = 8.6 units
Step 2: Let's calculate the distance from B to C, this way:
d = √4² - 0² + -7² - 0²
d = √4² - 7²
d = √16 + 49
d = √65
d = 8.06 units
Step 3: Let's calculate the distance from A to C, as follows:
d = √(4 - -5)² + (-7 - -7)²
d = √9² + 0²
d = √81
d = 9 units
Step 4: Let's calculate the distance from D to E, this way:
d = √(-1 - -6)² + (1 - -6)²
d = √5² + 7²
d = √25 + 49
d = √ 74
d = 8.6 units
Step 5: Let's calculate the distance from E to F, as follows:
d = √(5 - -1)² + (-8 -1) ²
d = √6² + -9²
d = √36 + 81
d = √117
d = 10.81 units
Step 6: Let's calculate the distance from D to F, this way:
d = √(5 - -6)² + (-8 - -6)²
d = √11² + -2²
d = √121 + 4
d = √125
d = 11.18 units
Step 7: We can conclude that only sides AB and DE are congruent, (8.6 units) but the other two sides of triangles ABC and DEF aren't congruent. Therefore, these two triangles are not congruent.
Now you can continue, following steps 1 to 7 to evaluate options B and C.
