Construct a triangle ABC in which AB = BC = AC = 7 cm. Measure ABC, BCA and BAC.

Question

ScanSolve AI Tutor · Accepted Answer

Huu hapa ni ufumbuzi wa swali la kwanza: "Construct a triangle ABC in which AB = BC = AC = 7 cm. Measure $\angle$ ABC, $\angle$ BCA and $\angle$ BAC."

Kwa kuwa pande zote za pembetatu ABC ni sawa (AB = BC = AC = 7 cm), hii ni pembetatu pacha (equilateral triangle). Katika pembetatu pacha, pembe zote za ndani ni sawa.

Chora mstari wa sentimita 7.
Chora mstari ulionyooka na uuweke alama A na B, urefu wake ukiwa sentimita 7.
Chora pinde mbili.
Weka ncha ya dira (compass) kwenye A na ufungue dira hadi sentimita 7. Chora upinde juu ya mstari AB. Kisha, weka ncha ya dira kwenye B (bila kubadilisha kipimo) na chora upinde mwingine juu ya AB, ukihakikisha unakata upinde wa kwanza.
Weka alama C na unganisha.
Weka alama ya makutano ya pinde hizo kama C. Unganisha A na C, na B na C kwa kutumia rula. Sasa una pembetatu ABC.
Pima pembe.
Kwa kuwa pembetatu ABC ni pacha, pembe zake zote za ndani ni sawa. Jumla ya pembe za ndani za pembetatu ni $180^\circ$ .
Kila pembe itakuwa:
$\frac{180^\circ}{3} = 60^\circ$
Hivyo, $\angle$ ABC = $60^\circ$ , $\angle$ BCA = $60^\circ$ , na $\angle$ BAC = $60^\circ$ .

Majibu:
$\boxed{\angle\text{ABC} = 60^\circ, \angle\text{BCA} = 60^\circ, \angle\text{BAC} = 60^\circ}$

Construct a triangle ABC in which AB = BC = AC = 7 cm. Measure ABC, BCA and BAC.

Step-by-step solution

Chora mstari wa sentimita 7.

Chora pinde mbili.

Weka alama C na unganisha.

Pima pembe.

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