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If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Based on the diagram above, the theorem can be written as follows.
This proof will be developed based on the given diagram, but it is valid for any pair of triangles.
If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Based on the diagram above, the theorem can be written as follows.
This proof will be developed based on the given diagram, but it is valid for any pair of triangles.
If the three sides of a triangle are congruent to the three sides of another triangle, then the triangles are congruent.
Based on the diagram above, the theorem can be written as follows.
This proof will be developed based on the given diagram, but it is valid for any pair of triangles.
The points C and F′′ are on opposite sides of AB. Now, consider CF′. Let G denote the point of intersection between AB and CF′′.
It can be noted that AC=AF′′ and BC=BF′′. By the Converse Perpendicular Bisector Theorem, AB is a perpendicular bisector of CF′′. Points along the perpendicular bisector are equidistant from the endpoints of the segment, so CG=GF′′.
If two angles and a non-included side of a triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
Based on the diagram above, the theorem can be written as follows.
This proof will be developed based on the given diagram, but it is valid for any pair of triangles.
It is given that two angles of △ABC are congruent to two angles of △BCD′′. Hence, by the Third Angle Theorem, ∠BCD′′ is congruent to ∠BCA.