Question
2 1 point State whether the triangles could be proven congruent, if possible, by SSS or SAS. Then, write a congruency statement. SSS, SAS, or neither: square "Write SSS, SAS, or neither Delta ADCcong Delta type your answer. "If the triangles are not congruentor cannot be proven congruent by SSS or SAS, write "not congruent"for "Remember to capitalize when needed
Answer
4
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Sophie
Elite · Tutor for 8 years
Answer
To determine if the triangles can be proven congruent by SSS (Side-Side-Side) or SAS (Side-Angle-Side), we need to analyze the given information about the quadrilateral ABCD.From the picture details, we know that AB = BC = CD = DA, which means that all four sides of the quadrilateral are congruent. This implies that ABCD is a rhombus. Since AC is connected, we have two triangles within the rhombus: triangle ADC and triangle ABC.Step 1: Identify congruent sidesWe know that AB = BC = CD = DA, so in triangles ADC and ABC:- AD = BC (because they are opposite sides of the rhombus)- AC = AC (common side to both triangles)- CD = AB (because they are opposite sides of the rhombus)Step 2: Identify congruent angles (if needed for SAS)Since ABCD is a rhombus, the diagonals bisect each other at right angles. Therefore, angle ADC and angle ABC are both right angles and are congruent.Step 3: Apply SSS or SASWe have three pairs of congruent sides (AD = BC, AC = AC, CD = AB), which satisfies the criteria for SSS congruency.Step 4: Write the congruency statementSince the triangles have three pairs of congruent sides, we can state that:
by SSS.Final Answer:SSS, SAS, or neither: SSS