{{ item.displayTitle }}

No history yet!

Student

Teacher

{{ item.displayTitle }}

{{ item.subject.displayTitle }}

{{ searchError }}

{{ courseTrack.displayTitle }} {{ statistics.percent }}% Sign in to view progress

{{ printedBook.courseTrack.name }} {{ printedBook.name }} If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

Based on the diagram above, the following relation holds true.

If $ABCD$ is a kite and $BA≅BC,$ then $∠A≅∠C$ and $∠B≆∠D.$

Consider a kite $ABCD$ such that $BA≅BC$ and draw the diagonal $BD.$ This diagonal divides the kite into two triangles.

By the Reflexive Property of Congruence, $BD≅BD.$ Then, the three sides of $△ABD$ are congruent to the three sides of $△CBD.$ $BD≅BDBA≅BCAD≅CD SideSideSide $ Therefore, $△ABD≅△CBD$ by the Side-Side-Side Congruence Theorem. Thus, by definition of congruent polygons, $∠C≅∠A.$ To prove that $∠B≆∠D,$ use indirect reasoning and assume temporarily that these angles are congruent. Since $∠A≅∠C,$ then the opposite angles of the kite are congruent. $∠A≅∠COpposite Angles∠B≅∠DOpposite Angles $ Then, Parallelogram Opposite Angles Theorem tells that the quadrilateral $ABCD$ is a parallelogram, which is a contradiction since it is a kite. This means that the temporary assumption is false implying that $∠B$ is not congruent to $∠D.$