Geometry | Unit 7 | Lesson 6: A Special Point | Practice Problems

How do the values of \(\alpha\) and \(\beta\) compare? Explain your reasoning.

Evaluate responses using AI:

OFF

Triangle \(ABC\) is shown together with its angle bisectors. Draw a point \(D\) that is equidistant from sides \(AC\) and \(BC\), but which is closest to side \(AB\).

Evaluate responses using AI:

OFF

In triangle \(ABC\), point \(D\) is the incenter. Sketch segments to represent the distance from point \(D\) to the sides of the triangle. How must these distances compare?

Evaluate responses using AI:

OFF

Triangle \(ABC\) has circumcenter \(D\). Sketch the 3 lines that intersect at the circumcenter. If the distance from point \(D\) to point \(A\) is 5 units, what is the distance from point \(D\) to point \(C\)? Explain or show your reasoning.

Evaluate responses using AI:

OFF

The angles of triangle \(ABC\) measure 50 degrees, 40 degrees, and 90 degrees. Will its circumcenter fall inside the triangle, on the triangle, or outside the triangle?

• inside the triangle

• on the triangle

• outside the triangle

Tyler and Kiran are discussing the parallelogram in the image. Tyler says the parallelogram cannot be cyclic. Kiran says the parallelogram can be cyclic if a circle is drawn carefully through the vertices. Do you agree with either of them? Explain or show your reasoning.

Evaluate responses using AI:

OFF

Find the measures of the remaining angles of quadrilateral \(WXYZ\).

Evaluate responses using AI:

OFF

Which expression describes a point that partitions a segment \(AB\) in a \(1:5\) ratio?

Write 3 expressions that can be used to find angle \(C\).

Evaluate responses using AI:

OFF