Question

question
use the diagrams below to answer the prompts.
answer
a=

by

b=

by

c=

by

submit answer

Explanation:

Step1: Analyze Diagram a

In diagram a, we have two right triangles. \( AB = EF \) (marked with one tick), \( BC = FD \) (marked with two ticks), and \( \angle B=\angle F = 90^\circ \). By SAS (Side - Angle - Side) congruence criterion, \( \triangle ABC\cong\triangle EFD \). So corresponding parts are equal.

Step2: Analyze Diagram b

In diagram b, \( AE \) is the perpendicular bisector of \( BC \) (since \( \angle AEB=\angle AEC = 90^\circ \) and \( E \) is on \( BC \)). Also, \( AB = AC = 7\) in (marked). So \( \triangle ABC \) is isosceles with \( AB = AC \), and \( BE=EC \) by the perpendicular bisector theorem.

Step3: Analyze Diagram c

In diagram c, we have two triangles with vertical angles at \( C \) (or the intersection point). Also, \( AB = CD \) (marked with one tick) and \( BC = DA \) (marked with one tick). By SAS (if we consider the vertical angles as the included angle) or SSS (since two sides are equal and the third side is common in terms of the intersection), the triangles are congruent.

Since the problem is about triangle congruence and properties (which falls under Geometry, a subfield of Mathematics), we can use the above analysis to fill in the blanks. But since the specific prompts for \( a \), \( b \), \( c \) are not clear (the dropdowns are not visible), assuming a common question like "Identify the congruence criterion for diagram a":

For diagram a, the congruence criterion is SAS.

Answer:

For diagram a, the congruence criterion is SAS (if the question was about congruence criterion for diagram a). (Note: Since the exact question in the dropdowns is not clear, this is a general answer based on the diagram analysis. If more specific details about the prompts for \( a \), \( b \), \( c \) are provided, the answer can be refined.)