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Name: ____________________________________________________________ Class: __________________ Foundations of Math 2 β Unit 4 Notes and Homework Packet Day 1: Basics of Geometry Congruent Congruent Segments Congruent Angles Midpoint Segment Bisector Angle Bisector Parallel Lines Perpendicular Lines Perpendicular Bisector Complementary Angles Supplementary Angles Linear Pairs Vertical Angles Right Angles Right Triangles Reflexive Property of Congruence Transitive Property of Congruence Draw the given pictures. Label all points. 1. K is the midpoint of GJ . 2. Lines β‘π΄π΅ and β‘πΆπ· intersect at point Q . Μ Μ Μ Μ Μ bisects β πΉππ. 3. ππ 4. One angle has a measure of 50o and another has a measure of xo. The two form a linear pair 5. Line l is perpendicular to m , and they intersect at point F . Line q is also perpendicular to m , intersecting at point B 6. οRTS and οMTS are complementary. β‘ bisects ππ Μ Μ Μ Μ 7. ππ 8. βπΊπ»π has 2 congruent angles, β πΊ and β π 9. Angles β πΈπ πΊ and β π½π π· are vertical angles. Μ Μ Μ Μ Μ and β‘ππ are parallel. Point 10. ππ Μ Μ Μ Μ Μ . G is the midpoint of ππ 11. One angles has a measure of x + 45o, another has a measure of 2xo, and a 3rd had an angle of x β 1o. All 3 make a linear pair. 12. βπΏπ½π is a right triangle, where β π is a right angle. β πΏ and β π½ are congruent. Day 2: Parallel Lines and Angle Relationships Parallel Lines: _______________________________________ Transversal: _________________________________________ Angle Relationships formed by a Parallel Line and a Transversal Corresponding Angles Alternate Interior Angles ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ Alternate Exterior Angles Consecutive Interior Angles ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ Practice: 1. 2. 3. 4. 5. 6. Classwork/Homework 4.2 Name the Angle Pair Relationships! Supplementary Angles, Vertical Angles, Alternate Interior Angles, Alternate Exterior Angles, Corresponding Angles, Consecutive Interior Angles, or No Relationship 1. Angles 1 and 4: _______________________________________ 2. Angles 1 and 5: _______________________________________ 3. Angles 4 and 5: _______________________________________ 4. Angles 6 and 7: _______________________________________ 5. Angles 5 and 7: _______________________________________ 6. Angles 6 and 8: _______________________________________ 7. Angles 2 and 8: _______________________________________ 8. Angles 2 and 6: _______________________________________ Day 3: Angles Relationship Proofs Vertical Angles are ___________________________ Corresponding Angles are ___________________________ Alternate Interior Angles are ___________________________ Alternate Exterior Angles are ___________________________ Consecutive Angles are ___________________________ Lines l and m are parallel. 1. If πβ 1 = 34°, what is πβ 4? 2. If πβ 2 = 3π₯ β 4° and πβ 4 = 5π₯ β 12°, what is the πβ 2? 3. If πβ 1 = 2π₯ β 19° and πβ 7 = 7π₯ + 1°, what is the πβ 1? 5. If πβ 3 = 8π₯ + 2° and πβ 7 = 2π₯ + 38°, what is the πβ 3? 4. If πβ 2 = 3π₯ + 5° and πβ 6 = 7π₯ β 15°, what is the πβ 6? 6. If πβ 2 = π₯ + 12° and πβ 5 = 6π₯°, what is the πβ 8? Classwork/Homework 4.3 1. 2. X = ____________ X = ____________ Reason: ___________________________________ Reason: ___________________________________ 3. 4. X = ____________ X = ____________ Reason: ___________________________________ Reason: ___________________________________ 5. 6. X = ____________ X = ____________ Reason: ___________________________________ Reason: ___________________________________ Reason: #2: ________________________________ Day 4: Triangle Sum Theorem Triangle Sum Theorem: ____________________________________________________________________ 1. 2. X = ________________ 3. X = ________________ 4. X = ________________ 5. X = ________________ 7. X = ________________ 6. X = ____________, Y = ____________, W = ____________ X = ____________ Y = ____________ W = ____________ Classwork/Homework 4.4 Use the triangle sum theorem to solve for the missing angles. 1. 2. __________________ 3. __________________ 4. __________________ 5. __________________ 6. _________________ __________________ 7. __________________ Day 5: Similar Triangles Similar Triangles have ________________________ ANGLES and __________________________ SIDES 3 Ways to Prove that 2 Triangles are SIMILAR: 1. ________________________________ (AA) - _________________________________________________ 2. ________________________________ (SAS) - ________________________________________________ 3. ________________________________ (SSS) - ________________________________________________ 1. Similar: 2. YES NO Similar: YES NO Reason: _________________ Reason: _________________ βππ π ~ β ________________ βπ΄π΅πΆ ~ β ________________ 3. Similar: 4. YES NO Similar: YES NO Reason: _________________ Reason: _________________ βπΏππ ~ β ________________ βπΊπ»πΉ ~ β ________________ 5. Similar: 6. YES NO Similar: YES NO Reason: _________________ Reason: _________________ βπ·π π΄ ~ β ________________ βπ·πΈπΉ ~ β ________________ 7. Similar: 8. YES NO Similar: YES NO Reason: _________________ Reason: _________________ βππ΄π ~ β ________________ βππΉπ ~ β ________________ 9. Similar: 10. YES NO Similar: YES NO Reason: _________________ Reason: _________________ βπ»ππ ~ β ________________ βπ΄π΅πΆ ~ β ________________ Classwork/Homework 4.5 Determine if the following triangles are similar. If so, give the reason and complete the similarity statement. 1. Similar: 2. YES NO Similar: YES NO Reason: _________________ Reason: _________________ βπππ ~ β ________________ βπππ ~ β ________________ 3. 4. Similar: YES NO Similar: YES NO Reason: _________________ Reason: _________________ βπΉπ π ~ β ________________ βπππ ~ β ________________ Day 6: Midsegment of a Triangle Midsegment of a Triangle: __________________________________________________________________ Formula: ________________________________________ 1. 2. x = _______________ 3. x = _______________ a. DE = 4x β 5 and BC = 3x + 15, then x = _________________ b. DE = 6x β 4 and BC = 4x + 8, then x = __________________ 4. 5. X = _______________ 6. X = _______________ 7. X = _______________ X = _______________ Classwork/Homework 4.6 Find the missing value using the midsegment theorem. 1. 2. X = _______________________ X = __________________________ 3. 4. X = _______________________ X = __________________________ 5. 6. X = _______________________ X = __________________________