Question

geometry test (20 questions)
final version with extra space for questions 11 - 20.
triangle inequality (4 problems)

1. do the side lengths 4, 5, and 8 create a triangle? explain.
2. do the side lengths 7, 10, and 18 create a triangle? explain.
3. if two sides are 5 and 7, what is the range of the third side?
4. if two sides are 8 and 12, what is the range of the third side?

ordering problems (6 problems)

1. in △abc, sides are ab = 5, bc = 7, and ac = 10. order the angles from least to greatest.
2. in △xyz, sides are xy = 9, yz = 11, and xz = 13. order the angles from least to greatest.
3. in △def, angles are ∠d = 40°, ∠e = 65°, ∠f = 75°. order the sides from least to greatest.
4. in △mno, angles are ∠m = 50°, ∠n = 70°, ∠o = 60°. order the sides from least to greatest.
5. in △ghi, sides are gh = 6, hi = 8, and gi = 9. order the angles from least to greatest.
6. in △jkl, angles are ∠j = 30°, ∠k = 75°, ∠l = 75°. order the sides from least to greatest.

Explanation:

11.

Step1: Aplicar la desigualdad triangular

La desigualdad triangular establece que para cualquier triángulo, la suma de las longitudes de cualquier par de lados debe ser mayor que la longitud del tercer lado. Comprobemos:
$4 + 5=9>8$, $4 + 8 = 12>5$, $5+8 = 13>4$.

Step1: Aplicar la desigualdad triangular

Comprobemos las sumas: $7+10 = 17<18$.

Step1: Usar la fórmula para el rango del tercer lado

Si $a$ y $b$ son las longitudes de dos lados de un triángulo, entonces $|a - b|$|7 - 5|=2$ y $7 + 5=12$.

Answer:

Sí, crean un triángulo.

12.