Triangle Properties and Constructions

This video tutorial covers Unit 7 Lesson 7 practice problems, focusing on geometric concepts such as the incenter, inscribed circles, and triangle areas. It explains how to calculate triangle areas using base and height, find angles using trigonometry, and construct the incenter. The video also explores properties of points on bisectors, discusses circumcenter and cyclic quadrilaterals, and demonstrates finding median intersections in triangles.

What is the incenter of a triangle?

• The point where the angle bisectors meet

• The point where the altitudes meet

• The point where the medians meet

• The point where the perpendicular bisectors meet

How do you calculate the area of triangle ACD?

• Base plus height

• Base plus height divided by two

• Base times height

• Base times height divided by two

What is the area of the entire triangle ABC?

• 56 units squared

• 46 units squared

• 26 units squared

• 36 units squared

How is angle A calculated in triangle ABC with an inscribed circle?

• Using cos inverse of adjacent over hypotenuse

• Using tan inverse of opposite over adjacent

• Using cot inverse of adjacent over opposite

• Using sin inverse of opposite over hypotenuse

What is the first step in constructing the inscribed circle of a triangle?

• Find the circumcenter

• Draw the perpendicular bisectors

• Draw the medians

• Find the incenter by constructing angle bisectors

What can be said about point D in relation to the sides of angle ACB?

• It is equidistant from all sides of the triangle

• It is closer to side BC

• It is closer to side AC

• It is equidistant from the sides AC and BC

How do you construct the incenter of a triangle?

• By constructing altitudes

• By constructing perpendicular bisectors

• By constructing medians

• By constructing angle bisectors

Where does the circumcenter fall in an obtuse triangle?

• At the centroid

• Outside the triangle

• Inside the triangle

• On the triangle

What determines if a park can have a water fountain equidistant from all corners?

• If the park is a cyclic quadrilateral

• If the park is a square

• If the park is a parallelogram

• If the park is a rectangle

How do you find the intersection of medians in a triangle?

• By using weighted averages

• By using angle bisectors

• By using perpendicular bisectors

• By using altitudes