Geometry Quiz

In the image below, ∠B is congruent to ∠C.

Tags

CCSS.8.G.A.2

Complete the statement below that proves that △ABC is an isosceles triangle. Begin by constructing a segment perpendicular to ______ that goes through point A, labeling the intersection point D. Since ∠BDA and ______ are both right angles, they are congruent to each other. ______ is congruent to itself and in both △ABD and △ACD. Two of the angles of △ABD are congruent to two of the angles of △ACD. Since the sum of the measures of the angles of a triangle is 180°, it follows that the third angles must be congruent. In other words, ∠BAD ≅ ______. Since ∠BDA ≅ ______, ______ ≅ ______, and ∠BAD ≅ ______, it follows that △ABD ≅ ______ by the ______ Triangle Congruency Theorem. Corresponding sides of congruent triangles are congruent, so ______ ≅ ______, making △ABC an isosceles triangle.

Tags

CCSS.HSG.SRT.B.5

The diagonals of quadrilateral ABCD bisect each other. Point E is the intersection of the diagonals.

Tags

CCSS.HSG.CO.C.11

Complete the statement below that proves that ABCD is a parallelogram. Because the diagonals of ABCD bisect each other, AE ≅ ______ and BE ≅ ______.

Tags

CCSS.HSG.CO.C.11

∠AEB ≅ ______ and ∠AED ≅ ______ because they are ______ angles.

Tags

CCSS.8.G.A.5

With AE ≅ CE, ∠AEB ≅ ∠CED, and BE ≅ DE, ΔAEB ≅ ______ by the Triangle Congruence Theorem.

Tags

CCSS.HSG.SRT.B.5

Corresponding parts of congruent triangles are congruent to each other, so it follows that ∠ABE ≅ ______.

Tags

CCSS.HSG.CO.B.7

Because the angles are ______ angles between lines AB and CD and transversal BD, it follows that the lines are parallel to each other.

Tags

CCSS.8.G.A.5

Similarly, with AE ≅ CE, ∠AED ≅ ∠CEB, and BE ≅ DE, ΔAED ≅ ______ by the Triangle Congruence Theorem.

Tags

CCSS.HSG.CO.B.7

Corresponding parts of congruent triangles are congruent to each other, so it follows that ∠DAE ≅ ______.

Tags

CCSS.HSG.CO.B.7