Geometry

Congruent and Similar Triangles

Triangles - Identify Congruent Triangles

         

In ABC\triangle ABC above, A=66,\angle A={66}^\circ, MM is the midpoint of side BC,\overline{BC}, and DD and EE are the feet of perpendicular drawn from MM to AB\overline{AB} and AC,\overline{AC}, respectively. If MD=ME,\lvert{\overline{MD}}\rvert=\lvert{\overline{ME}}\rvert, what is the measure of CME?\angle CME ?

Note: The above diagram is not drawn to scale.

Triangles ABCABC and DEFDEF are congruent, that is, ABCDEF. \triangle ABC \cong \triangle DEF . If AB=3AB=3, BC=4BC=4 and CA=5CA=5 , what is the length of DEDE?

In triangles ABCABC and DEFDEF, if we know that AB=EF,BC=DE AB = EF, BC = DE and ABC=DEF \angle ABC = \angle DEF , are the triangles congruent?

In triangles ABCABC and DEFDEF, if we know that ABC=DFE \angle ABC = \angle DFE , BCA=FED \angle BCA = \angle FED and CAB=EDF \angle CAB = \angle EDF , are the triangles congruent?

Triangles ABCABC and DEFDEF are congruent. If AB=DE AB = DE, BC=EF BC = EF , ABC=37 \angle ABC = 37 ^ \circ and EDF=39 \angle EDF = 39 ^ \circ , what is the measure (in degrees) of EFD \angle EFD?

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