Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Which of the following statements are true?
Create an answer using the numbers associated with the true statements. For example, if only 1, 2, and 5 are true, then the answer is 125; if only 3 and 5 are true, then the answer is 35, etc.
If a given statement does not contain names of geometrical objects, it is a general statement aboutcircles and is not necessarily related to the diagram.
1. CH−→ is a tangent of ⊙D
2. A tangent of a circle is perpendicular to the radius at the point of tangency.
3. BA−→is a secant of ⊙D
4. If two parallel lines intersect a circle, the intercepted arcs between those lines are congruent.
5. m∠ABF=mAB
6. m∠ABE=12⋅mAH
7. A secant is a line (segment, or ray) that intersects a circle in exactly one point.
Create an answer using the numbers associated with the true statements. For example, if only 1, 2, and 5 are true, then the answer is 125; if only 3 and 5 are true, then the answer is 35, etc.
If a given statement does not contain names of geometrical objects, it is a general statement about
1. CH−→ is a tangent of ⊙D
2. A tangent of a circle is perpendicular to the radius at the point of tangency.
3. BA−→is a secant of ⊙D
4. If two parallel lines intersect a circle, the intercepted arcs between those lines are congruent.
5. m∠ABF=mAB
6. m∠ABE=12⋅mAH
7. A secant is a line (segment, or ray) that intersects a circle in exactly one point.
a 23467
b1237
c 34567
d 3
e 1245
f 2346
Transcribed Image Text:In the diagram presented, we observe a geometric construction involving a circle and several lines interacting with it. The circle is centered at point \( D \).
Key elements of the diagram:
- **Circle**: The circle is drawn with center \( D \).
- **Points on the Circle**:
- Points \( B \) and \( G \) lie on the circumference of the circle.
- **Tangents and Extended Lines**:
- Line \( AB \) and line \( BC \) are extended tangents to the circle, meeting at point \( B \).
- Line \( EF \) is an extension that passes through point \( A \).
- Line \( CG \) extends through point \( G \).
- Line \( HE \) extends from point \( H \), meeting line \( FG \) at the extension.
- **Chord and Secant Line**:
- Line \( H \) lies on the circle, with \( DH \) and \( DG \) forming a chord intersecting the circle at point \( H \).
This diagram can demonstrate properties of tangents, chords, and secants in a circle, helpful for understanding key concepts in geometry, such as the tangent-secant relationships and angle measures associated with these configurations.
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