Triangle Inequality
To form a triangle, the sum of any two sides must be ______ the third side.
Greater than.
Find the hypotenuse of a right triangle with legs 6 and 8.
10
Vertical angles are always ______.
Congruent.
Sum of interior angles of any triangle:
180°
How what formula do you use to find diagonal distance?
a2+b2=c2
These side lengths: 5, 7, 12
can they form a triangle?
No, because 5 + 7 is not greater than 12.
A ladder reaches 12 ft high and is 9 ft from the wall. How long is the ladder?
15 ft
If ∠C = x + 10 and ∠D = 4x – 14 and they’re vertical, what is ∠D?
26°
A quadrilateral’s interior sum:
360°
Distance between (0,0) and (3,4).
5
Which set can form a triangle?
A) 2, 3, 10
B) 6, 7, 8
C) 4, 4, 12
B) 6, 7, 8
A rectangle base is 6 in × 8 in. What is the diagonal?
10 inches
Three angles form a straight line. If two angles are 30° and 80°, what is the third angle?
70°
Find the interior sum of a 14-sided polygon.
2,160°
Given triangle points on a grid, if two sides measure 5 units and 7 units, and the last side is 4 units, the perimeter is:
16 units
A builder has boards of 4 in, 9 in, and 15 in. Which board must be replaced to form a triangle?
Replace 15 in — too long.
A baton is 11 inches long. Can it fit across the rectangle’s base diagonal of 6 × 8?
No — diagonal is 10 inches.
In a triangle angles ∠1and ∠2 are remote interior angles to ∠3. Where ∠1=5x∘, ∠2=(4x-10)∘, and ∠3=(10x−20)∘. Find ∠3.
80
Find the interior sum of a 11-sided polygon (hendecagon).
1,620°
The school is at (4, 2) and the office is at (10, –1). What is the distance?
√45 or about 6.7 units
True or False: All equilateral triangles satisfy the triangle inequality.
True — all sides equal, so the sum of any two is greater than the third.
A 3D box is 6 × 8 × 6. What is the interior diagonal?
About 11.7 inches
If two angles are Complementary and one is 6x – 9 and the other is 3x + 18, find the measure of both angles.
45°
A polygon’s interior angle sum is 1,440°. How many sides does it have?
10 sides
Find the perimeter of a triangle with vertices
(–2, 1), (3, 1), and (3, 5).
About 15.4 units