Geo: Unit 7 Relationships with Triangles Unit 7 Relationships with Triangles

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Unit 7 Relationships with Triangles Target 7.1: Use the midsegment to determine unknown information of triangles Target 7.2: Apply perpendicular bisectors and angle bisectors to find unknowns 7.

1 Unit 7 Relationships with Triangles Target 7.1: Use the midsegment to determine unknown information of triangles Target 7.2: Apply perpendicular bisectors and angle bisectors to find unknowns 7.2a Perpendicular and Angle Bisectors 7.2b Construction of Perpendicular Bisectors and Angle Bisectors Date Target Assignment Done! R Worksheet F a 7.1 Mini-Quiz / 7.2a Worksheet M b 7.2b Worksheet T 1-10 Rev 7.2 Mini-Quiz / Unit 7 Review W 1-11 Rev Unit 7 Review R 1-12 Test Unit 7 Test NAME

2 Vocabulary: Midsegment: 7.1 Midsegment Target 1: Use the midsegment to determine unknown information of triangles (talk about proportional sides) Midsegment Theorem: Parallel to third side If a segment joins two triangle sides at their, then it is parallel to the. Midpoints; third side (p. 233) Midsegment Theorem: Length is half of third side If a segment joins two triangle sides at their midpoints, then its length is of the third side s length. One-half (p.233) Example 1: Applying the midsegment theorem In each triangle, M, N, and P are midpoints of the sides. Name the segment parallel to the one given. CD

3 Example 2: Applying the midsegment theorem Find the length of SR and FD. YOU TRY NOW! Find the missing length indicated. 1) Find CD 2) Find PQ 3) Find the length of QR and WY. 4) Find the sum of the lengths of SR and FD.

4 7.2a Construction of Perpendicular Bisectors and Angle Bisectors Target 2: Use perpendicular bisectors to establish a point of concurrency and find unknowns Concurrent intersecting at the same point When 3 or more segments, rays, or lines intersect at the same points, they are called. The point where they intersect is called a. Example 1: Construct a perpendicular bisector of a side in a triangle The point of concurrency for PERPENDICULAR BISECTORS is called: Circumcenter the point of concurrency for the perpendicular bisectors of a triangle

5 Example 2: Construct an angle bisector in a triangle The point of concurrency for ANGLE BISECTORS is called: Incenter the point of concurrency for the perpendicular bisectors of a triangle

6 7.2b Perpendicular and Angle Bisectors Target 2: Apply perpendicular bisectors and angle bisector to find unknowns Perpendicular Bisector Theorem IF a point is on a segment s perpendicular bisector, then it is the from the segments endpoints. Same distance Example 1: Applying the perpendicular bisector theorem What is the length of IB? Perpendicular Bisector Theorem Converse IF a point is the from the segment s endpoints, then it is on the segments. Same distance, perpendicular bisector Example 2: Applying the perpendicular bisector theorem Acrobat Andy is secured by two 7-meter ropes which are attached to the ends of a 4-meter bar. What is his vertical distance from the bar, to the nearest tenth?

7 Angle Bisector Theorem Angle Bisector a ray that bisects an angle, dividing it into two equal parts. IF a point is on the bisector of an angle, then that point is the distance from the sides that form that angle. Angle Bisector Theorem Converse If a point in the interior of an angle is the same distance from the angle s sides, then it is on the. ) Example 3: Applying the angle bisector theorem Find the value of x if PD = 4x + 10 and PC = 8.

8 YOU TRY NOW! Find the indicated measure. 1) Find the sum of QR and PQ. 2) Find DB. ***HINT: What s the Pythagorean theorem? 3) XP is an angle bisector. Find YXZ if m 2 = 4x + 5 and m 1 = 5x 2 4) PT is an angle bisector. If m 1 = 7x + 7 and m VTU = 16z + 4.

VOCABULARY. Chapters 1, 2, 3, 4, 5, 9, and 8. WORD IMAGE DEFINITION An angle with measure between 0 and A triangle with three acute angles.

VOCABULARY. Chapters 1, 2, 3, 4, 5, 9, and 8. WORD IMAGE DEFINITION An angle with measure between 0 and A triangle with three acute angles. Acute VOCABULARY Chapters 1, 2, 3, 4, 5, 9, and 8 WORD IMAGE DEFINITION Acute angle An angle with measure between 0 and 90 56 60 70 50 A with three acute. Adjacent Alternate interior Altitude of a Angle