CPCTC Proof Practice

Given: \overline{AC}\perp\overline{BD}, \overline{AD}\cong\overline{CD}

Prove: \angle{A}\cong\angle{C}

Statement Reason

1. \overline{AC}\perp\overline{BD}

2. \overline{AD}\cong\overline{CD}

3. \angle{ADB} and \angle{CDB} are rt \angle's

4. \angle{ADB}\cong\angle{CDB}

5. \overline{BD}\cong\overline{BD}

6. \triangle{ABD}\cong\triangle{CBD}

7. \angle{A}\cong\angle{C}

Given: \angle{EFH}\cong\angle{GHF}, \angle{EHF}\cong\angle{GFH}

Prove: \overline{HE}\cong\overline{FG}

Statement Reason

1. \angle{EFH}\cong\angle{GHF}

2. \angle{EHF}\cong\angle{GFH}

3. \overline{HF}\cong\overline{FH}

4. \triangle{EFH}\cong\triangle{GHF}

5. \overline{HE}\cong\overline{FG}

Given: Use Picture

Prove: \angle{K}\cong\angle{P}

Statement Reason

1. \angle{J}\cong\angle{N}

2. \angle{L} and \angle{M} are rt \angle's

3. \overline{JL}\cong\overline{NM}

4. \angle{L}\cong\angle{M}

5. \triangle{JLK}\cong\triangle{NMP}

6. \angle{K}\cong\angle{P}

Given: Use Picture

Prove: \angle{QST}\cong\angle{SQR}

Statement Reason

1. \angle{TQS}\cong\angle{RSQ}

2. \angle{T} and \angle{R} are rt \angle's

3. \angle{T}\cong\angle{R}

4.

5. \triangle{TQS}\cong\triangle{RSQ}

6.

Given: Use Picture

Prove: \angle{U}\cong\angle{W}

Statement Reason

1. \overline{UV}\cong\overline{WV}

2.

3.

4. \triangle{TQS}\cong\triangle{RSQ}

5.

Given: Use Picture

Prove: \overline{ZA}\cong\overline{CA}

Statement Reason

1. \overline{YA}\cong\overline{BA}

2.

3.

4. \triangle{YZA}\cong\triangle{BCA}

5.

Given: \overline{CB}\parallel\overline{ED}, \overline{CB}\cong\overline{ED}, C is the midpoint of \overline{AE}

Prove: \overline{AB}\parallel\overline{CD}

Statement Reason

1. \overline{CB}\parallel\overline{ED}

2. \overline{CB}\cong\overline{ED}

3. C is the midpoint of \overline{AE}

4. \overline{AC}\cong\overline{CE}

5.

6. \triangle{ABC}\cong\triangle{CDE}

7.

8. \overline{AB}\parallel\overline{CD}