9.04 Congruent triangle proofs
Complete the following proof to show that \triangle KLN and \triangle MNL are congruent:
\text{ } \\ \begin{array}{cll} ⬚ \text{ is common} & \\ KL = MN &\text{(⬚)} \\ \angle KLN = ⬚ &\text{ (Alternate angles in parallel lines)} \\ \triangle NKL \equiv \triangle LMN &\text{(⬚)} \end{array}
Prove that the following pairs of triangles are congruent:
\triangle PQR and \triangle STR
\triangle ABD and \triangle CBD
\triangle DEC and \triangle FEG
\triangle ACD and \triangle ACB
\triangle PFG and \triangle PYX
\triangle PQX and \triangle RQX
\triangle WXZ and \triangle YXZ
Given XZ bisects \angle WZY.
\triangle WBY and \triangle ZAX
Given XZ= WY.
Consider the adjacent figure:
Prove that \triangle ABC is congruent to \triangle DFE.
Find the side equal to the following:
Consider the adjacent figure:
Prove that \triangle LNM is congruent to \triangle LNP.
Find the side of equal to the following:
Consider the adjacent figure:
Prove that \triangle ADB is congruent to \triangle CBD.
Find the angle equal to the following:
\angle ABD
\angle BCD
Consider the adjacent figure:
Prove that \triangle PSQ is congruent to \triangle RQS.
Find the angle equal to the following:
\angle PSQ
\angle QSR
Consider the adjacent figure:
Prove that \triangle ABD is congruent to \triangle CBD.
Find the angle equal to the following:
\angle ADB
\angle BCD
Consider the adjacent figure:
Prove that \triangle NOM is congruent to \triangle POQ.
Find the angle equal to the following:
\angle NOM
\angle OPQ
Two straight lines AB and CD (unequal in length) are drawn so that they intersect at their midpoint E:
Prove that \triangle AED and \triangle BEC are congruent.
State which side is equal in length to:
State which angle has an equal size with:
Explain why \angle AED is equal to \angle BEC.
Consider the diagram where the triangles \triangle PQT and \triangle QRS are congruent and PR is a straight line segment:
Prove that \triangle PQT and \triangle QRS are congruent.
Is the triangle \triangle QST congruent to the triangles \triangle PQT and \triangle QRS? If yes, state what triangle congruence test they satisfy.
Consider the diagram where GD and FH are straight lines:
Prove that \triangle EFG and \triangle EHD are congruent.
Explain why FG \parallel HD.
Consider the diagram where QS is a straight line segment:
Prove that \triangle PQR and \triangle PSR are congruent.
Explain why \triangle PQS is isosceles.
