Using Common Parts Write a plan for a proof that does not use overlapping triangles. Given: angle ZXW congruent to angle YWX, angle ZWX congruent to angle YXW

Prove: ZW congruent to YX

Label point M where ZX intersects WY.

ZW congruent to YX by CPCTC if _

You can prove these triangles congruent using ASA as follows:

Look at triangle MWX. MW congruent to MX by the
Converse of the Isosceles Triangle Theorem

angle ZMW congruent to angle YMX because _ are congruent. By the Angle Addition Postulate, angle ZWM congruent to angle YXM. So triangle ZWM congruent to triangle YXM by _ So ZW congruent to YX by _

Choose the correct answers for the blanks.

Blank A: angle M is a right angle, triangle WMX is isosceles, angles W and X are congruent, or triangles ZWM and YXM are congruent

Blank A is an important step!

Blank B: reflexive prop. of congruence, all of these, verticals angles, or corresponding angles

Blank C: AAA, ASA, SSS, or SAS

Blank D: SAS, SSS, CPCTC, or symmetry prop. of congruence