Is there a rigid transformation that would map ΔABC to ΔDEC
2 answers:
Answer:
Both ΔABC and ΔDEC are congruent, therefore there a rigid transformation that would map ΔABC to ΔDEC.
Step-by-step explanation:
In rigid transformation the size and shape of the figure remain s the same if the original figure and transformed figure are congruent.
In ΔABC and ΔDEC,
(Given)
(Given)
(Given)
By AAS postulate of congruent triangle,
Since both ΔABC and ΔDEC are congruent, therefore there a rigid transformation that would map ΔABC to ΔDEC.
The diagram shows the 180 degree rotation about the point C and the rotation is a rigid transformation.
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The picture in the attached figure
step 1
we know that
It is given that AD and BD are bisectors of ∠CAB and ∠CBA respectively.
Therefore,
x = ∠CAB/2 -----> equation 1
y = ∠CBA/2 -----> equation 2
step 2
In triangle ABC,
∠CAB + ∠CBA + ∠ACB = 180° ----> [The sum of all three angles of a triangle is 180°]
∠CAB + ∠CBA + 110° = 180°
∠CAB + ∠CBA = 180° - 110°
∠CAB + ∠CBA = 70° ------> divide by 2 both sides
∠CAB/2 + ∠CBA/2 = 70/2 -------> equation 3
substitute equation 1 and equation 2 in equation 3
x+y=35
hence
the answer is
x+y =35°
⇒ x + y = 35° ...[From equation (1) and (2)]
step 1
we know that
It is given that AD and BD are bisectors of ∠CAB and ∠CBA respectively.
Therefore,
x = ∠CAB/2 -----> equation 1
y = ∠CBA/2 -----> equation 2
step 2
In triangle ABC,
∠CAB + ∠CBA + ∠ACB = 180° ----> [The sum of all three angles of a triangle is 180°]
∠CAB + ∠CBA + 110° = 180°
∠CAB + ∠CBA = 180° - 110°
∠CAB + ∠CBA = 70° ------> divide by 2 both sides
∠CAB/2 + ∠CBA/2 = 70/2 -------> equation 3
substitute equation 1 and equation 2 in equation 3
x+y=35
hence
the answer is
x+y =35°
⇒ x + y = 35° ...[From equation (1) and (2)]