Download Semester 1 Exam Review Name: Geometry 58) Given: and bisect

Semester 1 Exam Review
Geometry
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58) Given: 𝑬𝑰 and 𝑯𝑭 bisect each other at G.
Prove:  E ≅  I
Statements
Reasons
1) 𝐸𝐼 and 𝐻𝐹 bisect each other at G.
1) Given
2) 𝐸𝐺 ≅ 𝐺𝐼
2) Definition of segment bisector
3) 𝐻𝐺 ≅ 𝐺𝐹
4) EGF  HGI
5) ∆𝐸𝐺𝐹 ≅ ∆𝐼𝐺𝐻
6)  E ≅  I
3) Definition of segment bisector
4) Vertical angles are congruent.
5) SAS
6) CPCTC
59) Given: MJ  JK
KL  ML
JK  ML
Prove: JM  KL
Statements
Reasons
1) MJ  JK
1) Given
2) KL  ML
2) Given
3) JK  ML
4) J and L are right angles
3) Given
4) Definfition of perpendicular
5) ∆MJK and ∆KLM are right triangles
5) Definition of right triangles
6) 𝑀𝐾 ≅ 𝑀𝐾
7) ∆𝑀𝐽𝐾 ≅ ∆𝐾𝐿𝑀
6) Reflexive
7) HL
8) JM  KL
8) CPCTC
60) Given: ∆AED is isosceles with vertex ∠E
AB  CD
Prove: ∆BEC is isosceles
Statements
1)∆AED is isosceles with vertex ∠E
Reasons
1) Given
2) AB  CD
2) Given
3) 𝐴𝐸 ≅ 𝐸𝐷
4) ∠𝐴 ≅ ∠𝐷
5) ∆𝐸𝐴𝐵 ≅ ∆𝐸𝐷𝐶
3) Definition of isosceles triangle
4) Isosceles Triangle Thm. (If sides, then angles.)
5) SAS
6) 𝐵𝐸 ≅ 𝐶𝐸
7) ∆BEC is isosceles
6) CPCTC
7) Definition of isosceles triangle