QQuestionMathematics
QuestionMathematics
Triangle JKL and triangle PQR are shown above. If ∠J is congruent to ∠P, which of the following must be true in order to prove that triangles JKL and PQR are congruent?
A. ∠L ≅ ∠R and JL = PR
B. KL = QR and PR = JL
C. JK = PQ and KL = QR
D. ∠K ≅ ∠Q and ∠L ≅ ∠R
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:Let's solve this step by step using the triangle congruence criteria:
Step 2:: Understand Triangle Congruence
To prove two triangles are congruent, we need to establish that they have: - The same corresponding side lengths, OR - The same corresponding angles and at least one corresponding side
Step 3:: Analyze the Given Information
We know that $$\angle J \cong \angle P$$, which means these angles are equal.
Step 4:: Evaluate the Congruence Criteria
D. $$\angle K \cong \angle Q$$ and $$\angle L \cong \angle R
Let's examine each option systematically: - This does NOT guarantee full congruence - We're missing information about the third angle or side - This provides two equal sides - But we need a third piece of information to prove congruence - This provides two equal sides - This DOES satisfy the Side-Angle-Side (SAS) congruence criterion - We now have two sides and the included angle equal - This provides two equal angles - But we need a corresponding side to prove congruence
Step 5:: Conclusion
- Equal included angle ($$\angle J \cong \angle P$$)
Option C provides the Side-Angle-Side (SAS) congruence criterion:
Final Answer
C. JK = PQ and KL = QR must be true to prove the triangles are congruent.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students