Skills Practice Workbook - Glencoe

15–3
Paragraph Proofs
NAME DATE PERIOD
Skills Practice
Write a paragraph proof for each conjecture.
1. If �ABD is an isosceles triangle with base B�D�
and C is the midpoint of B�D�, then �ACD �
�ACB.
If �ABD is an isosceles triangle with base B�D�, then A�D� � A�B�. If C is the
midpoint of B�D�, then C�D� � C�B�. A�C� � A�C� by the Reflexive Property, so
�ACD � �ACB by SSS.
2. If lines a and b are parallel and W�X� � X�Y�,
then �WXS � �YXZ.
If lines a and b are parallel, then �SWX � �XYZ since they are alternate
interior angles. �WXS � �YXZ since they are vertical angles. Then it is
given that W�X� � X�Y�, so �WXS � �YXZ by ASA.
3. If ACDE is an isosceles trapezoid with bases
A�C� and E�D�, then �AED � �CDE.
If ACDE is an isosceles trapezoid with bases A�C� and E�D�, then the legs
are congruent, so A�E� � C�D�. Also, an isosceles trapezoid has congruent
base angles, so �AED � �CDE. Now,E�D� � E�D� by the Reflexive Property,
so �AED � �CDE by SAS.
4. If RSTX is a rhombus, then �RXT � �RST.
If RSTX is a rhombus, then RS � RX and XT � ST. RT � RT by the
Reflexive Property, so �RXT � �RST by SSS.
© Glencoe/McGraw-Hill 87 Geometry: Concepts and Applications
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