Proof: The Isosceles Triangle Base Angles Theorem (Geometry)
Free printable Geometry geometry worksheet: complete a two-column proof that the base angles of an isosceles triangle are congruent, using SAS and CPCTC.
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Geometry Proof: The Isosceles Triangle Base Angles Theorem
Complete each two-column proof that the base angles of an isosceles triangle are congruent, using the angle-bisector construction, SAS and CPCTC.
- 1.Triangle XYZ with XY ≅ XZ. Prove: ∠Y ≅ ∠Z. Complete the missing statement in step 1 of the two-column proof.
Statement Reason 1. Given 2.Draw XW, the bisector of ∠X, meeting YZ at W. Construction (every angle has exactly one bisector) 3.∠YXW ≅ ∠ZXW. Definition of an angle bisector 4.XW ≅ XW. Reflexive Property of Congruence 5.△YXW ≅ △ZXW. SAS (Side-Angle-Side) Congruence 6.∠Y ≅ ∠Z. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) - 2.Triangle PQR with PQ ≅ PR. Prove: ∠Q ≅ ∠R. Complete the missing statement in step 3 of the two-column proof.
Statement Reason 1.PQ ≅ PR. Given 2.Draw PS, the bisector of ∠P, meeting QR at S. Construction (every angle has exactly one bisector) 3. Definition of an angle bisector 4.PS ≅ PS. Reflexive Property of Congruence 5.△QPS ≅ △RPS. SAS (Side-Angle-Side) Congruence 6.∠Q ≅ ∠R. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) - 3.Triangle XYZ with XY ≅ XZ. Prove: ∠Y ≅ ∠Z. Complete the missing reason in step 6 of the two-column proof.
Statement Reason 1.XY ≅ XZ. Given 2.Draw XW, the bisector of ∠X, meeting YZ at W. Construction (every angle has exactly one bisector) 3.∠YXW ≅ ∠ZXW. Definition of an angle bisector 4.XW ≅ XW. Reflexive Property of Congruence 5.△YXW ≅ △ZXW. SAS (Side-Angle-Side) Congruence 6.∠Y ≅ ∠Z. - 4.Triangle EFG with EF ≅ EG. Prove: ∠F ≅ ∠G. Complete the missing statement in step 4 of the two-column proof.
Statement Reason 1.EF ≅ EG. Given 2.Draw EH, the bisector of ∠E, meeting FG at H. Construction (every angle has exactly one bisector) 3.∠FEH ≅ ∠GEH. Definition of an angle bisector 4. Reflexive Property of Congruence 5.△FEH ≅ △GEH. SAS (Side-Angle-Side) Congruence 6.∠F ≅ ∠G. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) - 5.Triangle ABC with AB ≅ AC. Prove: ∠B ≅ ∠C. Complete the missing statement in step 5 of the two-column proof.
Statement Reason 1.AB ≅ AC. Given 2.Draw AD, the bisector of ∠A, meeting BC at D. Construction (every angle has exactly one bisector) 3.∠BAD ≅ ∠CAD. Definition of an angle bisector 4.AD ≅ AD. Reflexive Property of Congruence 5. SAS (Side-Angle-Side) Congruence 6.∠B ≅ ∠C. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) - 6.Triangle JKL with JK ≅ JL. Prove: ∠K ≅ ∠L. Complete the missing statement in step 6 of the two-column proof.
Statement Reason 1.JK ≅ JL. Given 2.Draw JM, the bisector of ∠J, meeting KL at M. Construction (every angle has exactly one bisector) 3.∠KJM ≅ ∠LJM. Definition of an angle bisector 4.JM ≅ JM. Reflexive Property of Congruence 5.△KJM ≅ △LJM. SAS (Side-Angle-Side) Congruence 6. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) - 7.Triangle JKL with JK ≅ JL. Prove: ∠K ≅ ∠L. Complete the missing statement in step 2 of the two-column proof.
Statement Reason 1.JK ≅ JL. Given 2. Construction (every angle has exactly one bisector) 3.∠KJM ≅ ∠LJM. Definition of an angle bisector 4.JM ≅ JM. Reflexive Property of Congruence 5.△KJM ≅ △LJM. SAS (Side-Angle-Side) Congruence 6.∠K ≅ ∠L. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) - 8.Triangle JKL with JK ≅ JL. Prove: ∠K ≅ ∠L. Complete the missing reason in step 1 of the two-column proof.
Statement Reason 1.JK ≅ JL. 2.Draw JM, the bisector of ∠J, meeting KL at M. Construction (every angle has exactly one bisector) 3.∠KJM ≅ ∠LJM. Definition of an angle bisector 4.JM ≅ JM. Reflexive Property of Congruence 5.△KJM ≅ △LJM. SAS (Side-Angle-Side) Congruence 6.∠K ≅ ∠L. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) - 9.Triangle ABC with AB ≅ AC. Prove: ∠B ≅ ∠C. Complete the missing statement in step 1 of the two-column proof.
Statement Reason 1. Given 2.Draw AD, the bisector of ∠A, meeting BC at D. Construction (every angle has exactly one bisector) 3.∠BAD ≅ ∠CAD. Definition of an angle bisector 4.AD ≅ AD. Reflexive Property of Congruence 5.△BAD ≅ △CAD. SAS (Side-Angle-Side) Congruence 6.∠B ≅ ∠C. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) - 10.Triangle ABC with AB ≅ AC. Prove: ∠B ≅ ∠C. Complete the missing reason in step 1 of the two-column proof.
Statement Reason 1.AB ≅ AC. 2.Draw AD, the bisector of ∠A, meeting BC at D. Construction (every angle has exactly one bisector) 3.∠BAD ≅ ∠CAD. Definition of an angle bisector 4.AD ≅ AD. Reflexive Property of Congruence 5.△BAD ≅ △CAD. SAS (Side-Angle-Side) Congruence 6.∠B ≅ ∠C. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
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