ADVANCED GEOMETRY 3.4 Beyond CPCTC Learner Objective:

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Presentation transcript:

ADVANCED GEOMETRY 3.4 Beyond CPCTC Learner Objective: LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC. Definition: A segment is drawn from a vertex of a triangle extending to the opposite side. If the segment is a MEDIAN then it bisects the side to which it is drawn. If the segment bisects the side to which it is drawn, then it is a MEDIAN.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC. NOTE: The point where the three medians meet is called the CENTROID. Label this point F.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC. Definition: A segment is drawn from a vertex of a triangle extending to the opposite side,   extended if necessary. If the segment is an ALTITUDE, then it is perpendicular the side to which it is drawn. If the segment is perpendicular the side to which it is drawn, then it is an ALTITUDE.

of triangles and will write proofs requiring steps beyond CPCTC. LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC. NOTE: The point where all three altitudes meet is called the ORTHOCENTER.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.

What additional line segments would enable us to complete this proof? LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC. Given: A M B O Prove: What additional line segments would enable us to complete this proof? Can we just draw them ourselves? Why? POSTULATE: Two points determine a line (or ray or segment).

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC. Given: A M B O Prove: STATEMENTS REASONS

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC. Assignment Pg. 135 # 4,5,7-9,11,12

of triangles and will write proofs requiring steps beyond CPCTC. LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC. STATEMENTS REASONS

of triangles and will write proofs requiring steps beyond CPCTC. LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC. STATEMENTS REASONS

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.

LEARNER OBJECTIVE: Students will apply properties of medians and altitudes  of triangles and will write proofs requiring steps beyond CPCTC.