Circumcenter of a Triangle Practice

Mathematical Equivalence

ON

Answer explanation

Circumcenters are equidistant to the vertices of the triangle, so the segments that go from the circumcenter to the vertices are congruent.

Tags

CCSS.MATH.CONTENT.HSG.SRT.C.8

Mathematical Equivalence

ON

Answer explanation

You'll need to solve for x, then plug it back in.

Tags

CCSS.MATH.CONTENT.HSG.SRT.C.8

Mathematical Equivalence

ON

Answer explanation

You'll need the Pythagorean Theorem to find CG or DG, then double it for the full side.

Tags

CCSS.MATH.CONTENT.HSG.SRT.C.8

Mathematical Equivalence

OFF

Answer explanation

Since circumcenters are created by perpendicular bisectors, the sides have been cut into two congruent segments. You'll solve for x and plug it in, then use the Pythagorean Theorem to find PD (which is congruent to other segments that are equidistant to the vertices).

Tags

CCSS.MATH.CONTENT.HSG.SRT.C.8

Mathematical Equivalence

ON

Answer explanation

The sides have been bisected, to you will have two congruent segments. You will solve for x and plug it back in to one of the expressions. That will give you half that side.

Tags

CCSS.MATH.CONTENT.HSG.SRT.C.8

Mathematical Equivalence

ON

Answer explanation

Use the Pythagorean Theorem to find KR (which is congruent to RM since the sides were bisected).

Tags

CCSS.MATH.CONTENT.HSG.SRT.C.8

Mathematical Equivalence

ON

Answer explanation

Use the length of DJ (or EJ) to use the Pythagorean Theorem to find DH (or EH). Find the full length of DE and set it equal to the expression for DE to solve for x.

Tags

CCSS.MATH.CONTENT.HSG.SRT.C.8

Mathematical Equivalence

ON

Answer explanation

You will do the Pythagorean Theorem twice, once for BK, then another for KF.

Tags

CCSS.MATH.CONTENT.HSG.SRT.C.8

Mathematical Equivalence

ON

Answer explanation

You will need the Pythagorean Theorem to find the length of a segment congruent to SZ.

Tags

CCSS.MATH.CONTENT.HSG.SRT.C.8

Mathematical Equivalence

ON

Answer explanation

All sides of the triangle are bisected. Perimeter is the sum of all sides.

Tags

CCSS.MATH.CONTENT.HSG.SRT.C.8