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

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

Tags

CCSS.HSG.SRT.B.5

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 \(AB\).

Tags

CCSS.HSG.C.A.3

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?

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.C.A.3

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

Tags

CCSS.HSG.C.A.3

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.

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

Tags

CCSS.HSG.C.A.2

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

Tags

CCSS.HSG.GPE.B.6

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

Tags

CCSS.HSG.SRT.C.8