How do you find the orthocenter of a triangle?

To find the orthocenter, construct the altitudes from each vertex to the opposite side. The point where all three altitudes intersect is the orthocenter.

What is the significance of the centroid in a triangle?

The centroid is the center of mass of the triangle and is the point where the triangle balances perfectly.

What is the formula for finding the length of a median in a triangle?

The length of a median can be calculated using the formula: $$m_a = \frac{1}{2} \times \text{sqrt}(2b^2 + 2c^2 - a^2)$$ , where a, b, and c are the lengths of the sides of the triangle.

What is the relationship between the circumcenter and the circumradius?

The circumradius is the radius of the circumcircle, which is the circle that passes through all three vertices of the triangle. The circumcenter is the center of this circle.

What is the relationship between the incenter and the incircle?

The incenter is the center of the incircle, which is the circle that is tangent to all three sides of the triangle.

If point M represents the circumcenter, what does it indicate about the triangle?

If point M is the circumcenter, it indicates that the triangle can be inscribed in a circle, meaning all vertices lie on the circumference of that circle.

What is the formula for finding the area of a triangle using the lengths of the medians?

The area of a triangle can be calculated using the formula: $$A = \frac{4}{3} \times \text{sqrt}(s(s-m_a)(s-m_b)(s-m_c))$$ , where s is the semi-perimeter and m_a, m_b, m_c are the lengths of the medians.

What is the significance of the points of concurrency in a triangle?

The points of concurrency (centroid, circumcenter, orthocenter, incenter) provide important information about the triangle's properties, such as balance, symmetry, and inscribed circles.

5.1/5.2 practice CW Center of triangles

Flashcard

•

Mathematics

•

9th - 10th Grade

•

Practice Problem

•

Hard

•

CCSS

HSG.C.A.3, HSG.CO.C.10, 6.G.A.1

Standards-aligned

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FLASHCARD QUESTION

Front

What is the centroid of a triangle?

Back

The centroid is the point of concurrency of the medians of a triangle. It is the point where the three medians intersect and is located two-thirds of the distance from each vertex to the midpoint of the opposite side.

Tags

CCSS.HSG.CO.C.10

FLASHCARD QUESTION

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point of concurrency of the perpendicular bisectors of the sides of a triangle. It is equidistant from all three vertices of the triangle.

Tags

CCSS.HSG.C.A.3

FLASHCARD QUESTION

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point of concurrency of the altitudes of a triangle. It can be located inside, on, or outside the triangle depending on the type of triangle.

Tags

CCSS.HSG.CO.C.10

FLASHCARD QUESTION

Front

What is the incenter of a triangle?

Back

The incenter is the point of concurrency of the angle bisectors of a triangle. It is equidistant from all three sides of the triangle.

Tags

CCSS.HSG.C.A.3

FLASHCARD QUESTION

Front

If V is the centroid of triangle RST and SV = 6, what is the length of UV if UT = 7.5?

Back

UV = 3.

Tags

CCSS.HSG.CO.C.10

FLASHCARD QUESTION

Front

What is the relationship between the lengths of segments created by the centroid on a median?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Tags

CCSS.HSG.CO.C.10

FLASHCARD QUESTION

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle. The point where they intersect is the circumcenter.

Tags

CCSS.HSG.C.A.3

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