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Overview

Solutions: Section 2.5 (Angle Introduction)

April 10, 2024
1 min read
solutions angles vertex

Figure it Out (Page 19)

Q1. Can you find the angles in the given pictures? Draw the rays forming any one of the angles and name the vertex of the angle.

Solution:

  • Yes. For example, in the bicycle frame, one angle is ∠BDC\angle BDC (referring to the triangle frame).
  • Vertex: DD.
  • Rays: DC→\overrightarrow{DC} and DB→\overrightarrow{DB}.

Q2. Draw and label an angle with arms ST and SR.

Solution:

  • Draw a point SS.
  • Draw two rays originating from SS: ST→\overrightarrow{ST} and SR→\overrightarrow{SR}.
  • The angle is ∠TSR\angle TSR or ∠RST\angle RST.

Q4. Name the angles marked in the given figure.

Solution:

  • ∠RTQ\angle RTQ
  • ∠RTP\angle RTP

Q5. Mark any three points on your paper that are not on one line. Label them A, B, C. Draw all possible lines going through pairs of these points.

  • How many lines do you get? Name them.
  • How many angles can you name using A, B, C? Write them down.

Solution:

  • Lines: We get three lines: AB↔,BC↔,CA↔\overleftrightarrow{AB}, \overleftrightarrow{BC}, \overleftrightarrow{CA}.
  • Angles: Using points A, B, and C, we can name three angles:
    1. ∠ABC\angle ABC (or ∠CBA\angle CBA)
    2. ∠BCA\angle BCA (or ∠ACB\angle ACB)
    3. ∠CAB\angle CAB (or ∠BAC\angle BAC)

Q6. Now mark any four points on your paper so that no three of them are on one line. Label them A, B, C, D.

  • Draw all possible lines. How many?
  • Name angles using A, B, C, D.

Solution:

  • Lines: We get six lines: AB↔,BC↔,CD↔,DA↔,AC↔,BD↔\overleftrightarrow{AB}, \overleftrightarrow{BC}, \overleftrightarrow{CD}, \overleftrightarrow{DA}, \overleftrightarrow{AC}, \overleftrightarrow{BD}.
  • Angles: We can name angles such as ∠BAC,∠CAD,∠BAD,∠ADB,∠BDC,∠ADC,∠DCA,∠ACB,∠DCB,∠CBD,∠DBA,∠CBA\angle BAC, \angle CAD, \angle BAD, \angle ADB, \angle BDC, \angle ADC, \angle DCA, \angle ACB, \angle DCB, \angle CBD, \angle DBA, \angle CBA.