Geometry 1 – Unit Five: Congruent Triangles, Practice
1. 2. If Δ PQR ≅ Δ STU, then PR ≅ __________ and ∠ Q ≅ ∠ __________ .
What does CPCTC stand for?
Use the diagrams to the right to answer Questions #3 – #13.
3.
If XY ≅ TS , ∠ Y ≅ ∠ S , and ∠ Z ≅ ∠ U , which method can be used to prove that Δ XYZ ≅ Δ TSU? If XY ≅ TS , YZ ≅ SU , and ∠ Y ≅ ∠ S , Y which method can be used to prove that Δ XYZ ≅ Δ TSU? If XY ≅ TS , XZ ≅ TU , and ZY ≅ US , which method can be used to prove that Δ XYZ ≅ Δ TSU?
X
S T
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5.
Z
U
6.
If ∠ Y ≅ ∠ S , ∠ Z ≅ ∠ U , and ZY ≅ US , which method can be used to prove that Δ XYZ ≅ Δ TSU? If ∠ Y and ∠ S are right angles, XZ ≅ TU , and YX ≅ ST , which method can be used to prove that Δ XYZ ≅ Δ TSU? If ∠ X ≅ ∠ T , XZ ≅ TU , and YZ ≅ SU , that Δ XYZ ≅ Δ TSU? which method can be used to prove
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If XY ≅ TS and ∠ Y ≅ ∠ S, which pair of segments or angles must be congruent to use the ASA method to prove Δ XYZ ≅ Δ TSU? If ∠ X ≅ ∠ T and XZ ≅ TU , which pair of segments or angles must be congruent to use the AAS method to prove Δ XYZ ≅ Δ TSU? If ∠ Z ≅ ∠ U and XZ ≅ TU , which pair of segments or angles must be congruent to use the SAS method to prove Δ XYZ ≅ Δ TSU? If ∠ Y and ∠ S are right angles and YZ ≅ SU , which pair of segments or angles must be congruent to use the HL method to prove Δ XYZ ≅ Δ TSU? If ZY ≅ US and ZX ≅ UT , which pair of segments or angles must be congruent to use the SSS method to prove Δ XYZ ≅ Δ TSU?
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Fill in the reasons for the following proof, using the diagram to the right.
14. GIVEN: AB DC ; BC AD PROVE: Δ ABD ≅ Δ CDB
4 1
3
2
STATEMENTS 1)
REASONS 1) 2) If lines are ||, then _____________________
AB DC
2) ∠ 1 ≅ ∠ ____________ 4) ∠ 2 ≅ ∠ ____________
3) _______________________________________ 3) Given 4) ____________________________________
5) _______________________________________ 5) Reflexive 6) Δ ABD ≅ Δ CDB 6) ____________________________________
Fill in the reasons for the following proof, using the diagram to the right.
P
15.
GIVEN: PN ⊥ MO; PM ≅ PO PROVE: Δ PNM ≅ Δ PNO
M
N
O
STATEMENTS 1)
PN ⊥ MO
REASONS 1) 2) ____________________________________ 4) ____________________________________
2) ∠ PNM and ∠ PNO are right angles 4)
PM ≅ PO
5) _______________________________________ 5) Reflexive 6) Δ PNM ≅ Δ PNO 6) ____________________________________
Fill in the reasons for the following proof, using the diagram to the right.
16. GIVEN: IJ ≅ KJ ; IL ≅ KL PROVE: ∠ I ≅ ∠ K
I L K J
STATEMENTS 1)
IJ ≅ KJ
REASONS 1) ____________________________________
2) _______________________________________ 2) Given 3) _______________________________________ 3) ____________________________________ 4) Δ ____________ ≅ Δ ____________ 5) ∠ I ≅ ∠ K 4) ____________________________________ 5) ____________________________________
Fill in the reasons for the following proof, using the diagram to the right.
17. GIVEN: QM PO; MN ≅ PN PROVE: QN ≅ ON
STATEMENTS 1) QM PO 2) ∠ Q ≅ ∠ ____________ 3) ∠ MNQ ≅ ∠ ____________ 5) Δ MNQ ≅ Δ ____________
REASONS 1) ____________________________________ 2) If lines are ||, then ______________________ 3) ____________________________________
4) _______________________________________ 4) Given 5) ____________________________________
6) _______________________________________ 6) ____________________________________
************************ANSWERS************************
1. 2. 3. 5. 7. 9. 11. 13. 14.
PR ≅ SU and ∠ Q ≅ ∠ T Corresponding Parts of Congruent Triangles are Congruent AAS SSS HL ∠X≅∠T
YZ ≅ SU YX ≅ ST
4. 6. 8. 10. 12.
SAS ASA The triangles are not congruent ∠Y≅∠S
XZ ≅ TU
AB DC -- Given ∠ 1 ≅ ∠ 3 -- If lines are ||, then alternate interior ∠s are ≅ BC AD -- Given ∠ 2 ≅ ∠ 4 -- If lines are ||, then alternate interior ∠s are ≅ BD ≅ BD -- Reflexive Δ ABD ≅ Δ CDB -- ASA
PN ⊥ MO -- Given ∠ PNM and ∠ PNO are right angles -- Definition of ⊥ PM ≅ PO -- Given PN ≅ PN -- Reflexive Δ PNM ≅ Δ PNO -- HL IJ ≅ KJ -- Given IL ≅ KL -- Given LJ ≅ LJ -- Reflexive Δ ILJ ≅ Δ KLJ -- SSS ∠ I ≅ ∠ K -- CPCTC
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QM PO -- Given ∠ Q ≅ ∠ O -- If lines are ||, then alternate interior ∠s are ≅ ∠ MNQ ≅ ∠ PNO -- Vertical ∠s are ≅ MN ≅ PN -- Given Δ MNQ ≅ Δ PNO -- AAS QN ≅ ON -- CPCTC