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Questions and Answers
What is the geometric definition of a midpoint?
The midpoint of a segment is the point that divides the segment into two congruent segments.
How many mid points does a segment have?
A segment has only one midpoint.
If a segment has an odd number of points, can it have a midpoint?
No, a segment with an odd number of points does not have a midpoint since the midpoint is the point that divides the segment into two congruent segments.
Segments have
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Segment
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Midpoint of a
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In angle PQR ,angle P=70°,angle Q=65° than find angle R?
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Given an angle PQR where angle P is 70° and angle Q is 65°, what is the measure of angle R?
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If angle PQR is a triangle, what is the sum of the measures of the interior angles of the triangle?
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What is the relationship between angles P, Q, and R in triangle PQR?
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Study Notes
Geometric Definitions and Concepts
- A midpoint of a segment is defined as the point that divides the segment into two equal lengths.
- A line segment has exactly one midpoint regardless of the number of points on it.
- A segment cannot have a midpoint if it contains an odd number of points, as midpoints require equal division.
Angle Measures in Triangle PQR
- In triangle PQR, if angle P measures 70° and angle Q measures 65°, angle R can be calculated.
- The measure of angle R is determined using the triangle angle sum property, which states that the sum of the interior angles of a triangle equals 180°.
- Therefore, angle R can be calculated as follows:
- ( R = 180° - (P + Q) = 180° - (70° + 65°) = 180° - 135° = 45° )
Relationship between Angles in Triangle PQR
- The relationship shows that the interior angles of triangle PQR (angles P, Q, and R) sum to 180°.
- This fundamental property applies universally to all triangles, highlighting the connection between the angles within triangle PQR.
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Description
Test your knowledge about midpoints of segments with this quiz. Explore the concept of midpoints, their geometric definition, and their presence in segments with odd numbers of points.
