Question

SEGMENTS, ANGLES, AND TRIANGLES Finding counterexamples to conjectures Show that each statement is false by providing a counterexample. (a) If the length of $\overline{AC}$ is 40 and point B lies on $\overline{AC}$, then AB = 26 and BC = 14. Counterexample: AB = BC = (b) If the perimeter of a rectangle is 48, then the length is 12 and the width is 12. Counterexample: length = width = (c) If $\angle 1$ and $\angle 2$ are complementary angles, then one of them must have a measure less than 45°. Counterexample: $m\angle 1$ = $m\angle 2$ = (d) If the measures of $\angle R$, $\angle S$, and $\angle T$ sum to 180°, then one of the angles must be obtuse. Counterexample: $m\angle R$ = $m\angle S$ = $m\angle T$ =

          SEGMENTS, ANGLES, AND TRIANGLES
Finding counterexamples to conjectures
Show that each statement is false by providing a counterexample.
(a) If the length of $\overline{AC}$ is 40 and point B lies on $\overline{AC}$, then AB = 26 and BC = 14.
Counterexample: AB =  BC = 
(b) If the perimeter of a rectangle is 48, then the length is 12 and the width is 12.
Counterexample: length =  width = 
(c) If $\angle 1$ and $\angle 2$ are complementary angles, then one of them must have a
measure less than 45°.
Counterexample: $m\angle 1$ =  $m\angle 2$ = 
(d) If the measures of $\angle R$, $\angle S$, and $\angle T$ sum to 180°, then one of the angles must
be obtuse.
Counterexample: $m\angle R$ =  $m\angle S$ =  $m\angle T$ =

SEGMENTS, ANGLES, AND TRIANGLES
Finding counterexamples to conjectures
Show that each statement is false by providing a counterexample.
(a) If the length of AC is 40 and point B lies on AC, then AB = 26 and BC = 14.
Counterexample: AB = BC =
(b) If the perimeter of a rectangle is 48, then the length is 12 and the width is 12.
Counterexample: length = width =
(c) If ∠ 1 and ∠ 2 are complementary angles, then one of them must have a
measure less than 45°.
Counterexample: m∠ 1 = m∠ 2 =
(d) If the measures of ∠ R, ∠ S, and ∠ T sum to 180°, then one of the angles must
be obtuse.
Counterexample: m∠ R = m∠ S = m∠ T =

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