ydutfiygouhpio[pofhcghjk
in Geometry Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

We can prove congruency this way. Let the intersection point be X so we have 4 triangles: AXC, AXD, CXB, BXD. Together AXC and AXD make triangle ADC, and CXB and BXD make BDC.

AXC and CXB are congruent because they share side CX, angle CXA=CXB=90°, AX=XB because CD is the perpendicular bisector of AB. Also, by Pythagoras, the hypotenuses AC and CB are equal. We can apply the same reasoning to triangles AXD and BXD, where the common side is XD, angles AXD and DXB=90°, and AX=XB. So we have two pairs of congruent triangles, so the combined triangles ADC and BDC are congruent.

We also have AC=CB and AD=DB (hypotenuses of the smaller triangles) and CD is common, so we have 3 sides SSS of the two triangles ADC and BDC proved congruent. 

by Top Rated User (774k points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,240 questions
90,465 answers
2,120 comments
78,574 users