Answered Which rule explains why these triangles are congruent?
K
65
Time
elapsed
17
SmartScore
out of 1000
85
999
N
SSS
ASA
SAS
AAS
These triangles cannot be
proven congruent.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Step-by-step explanation:

  The triangles cannot be proven congruent.

Step-by-step explanation:

Two adjacent sides and an angle not between them (the vertical angles in the middle) are congruent, but SSA is not a guarantee of triangle congruence.

The triangles cannot be proven congruent.

Additional comment

If it can be shown that sides NP and KM are the longest sides, then an argument can be made for SSA congruence (not a choice). There is nothing in the figure or problem statement to indicate such an argument is supported.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.