In triangles ABC and LMN, ∠A ≅ ∠L, ∠B ≅ ∠M, and ∠C ≅ ∠N. Is this information sufficient to prove triangles ABC and LMN congruent through ASA? Explain your answer.

(see below)

Step-by-step explanation:

No, this is not enough info.

Why?

All three angles may be congruent, but this doesn't prove that the sides are also congruent to each other. For instance, the angles may have the same measures but the sides may not. See the attached image for more specifics.

The only way you can tell two triangles are congruent when given congruence statement are these three triangle congruence theorems:

SSS (side-side-side) Theorem—if all three sides of both triangles are congruent, then the two triangles are congruent.

ASA (angle-side-angle) Theorem—if two corresponding angles and their attaching side of both triangles are congruent, then the two triangles are congruent.

SAS (side-angle-side) Theorem—if two corresponding sides and the included angle of two triangles are congruent, then the two triangles are congruent.

2160ft3

step-by-step explanation:

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180