As shown in the graph, ΔGHI ≅ ΔG'H'I', since this is a vertical shift, and ΔG'H'I' ≅ ΔG''H''I'', since this is a horizontal shif
t.
We can also show that triangles GHI and G''H''I'' are congruent directly, by using the translation
A) (x, y) → (x + 3, y - 4).
B) (x, y) → (x - 3, y + 1).
C) (x, y) → (x + 2, y + 2).
D) (x, y) → (x + 4, y - 5).
We can also show that triangles GHI and G''H''I'' are congruent directly, by using the translation
A) (x, y) → (x + 3, y - 4).
B) (x, y) → (x - 3, y + 1).
C) (x, y) → (x + 2, y + 2).
D) (x, y) → (x + 4, y - 5).
1 answer:
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Answer:
a) Acute triangle
b) Right triangle
Step-by-step explanation:
∵ A triangle having sides a, b and c is called,
Acute : If a² + b² > c² or a² + c² > b² or b² + c² > a²,
Obtuse : if a² + b² < c² or a² + c² < b² or b² + c² < a²
Right : a² + b² = c² or a² + c² = b² or b² + c² = a²,
a) Let A≡(-1, 1), B≡(7,-2) and C≡(1,-5),
By the distance formula,
Similarly,
∵ The sum of any two sides is greater than third side,
So, ABC is a triangle,
Now,
⇒ ABC is an acute triangle.
b) Let P≡(0,6), Q≡(1,2) and R≡(5,3),
By the distance formula,
PQ = √17 unit,
QR = √17 unit,
RP = √34 unit,
∵ The sum of any two sides of PQR is greater than third side,
⇒ PQR is a triangle ,
Also,
Hence, PQR is a right triangle.