Question

watch the video below to learn how the properties of different quadrilaterals (a polygons with

1. intersection of diagonals, parallelograms, rectangles, squares, rhombus, and piles
2. proving properties of parallelogram with two - column proofs

math nation digital textbook:
click each link below to learn the concepts. each component includes a video and you can select y
student fl geometry -> proving relationships and theorems -> proving properties of parallelogra
student fl geometry -> proving relationships and theorems -> proving properties of parallelogra
then, answer \check your understanding\ assignment below. you have three attempts.
8.1.7 check your understanding
complete the two - column proof.
given: rwkg is a parallelogram.
prove: $\triangle rwk \cong \triangle kgr$

Explanation:

Step1: List given & parallelogram props

Given: $RWKG$ is a parallelogram.
In a parallelogram, opposite sides are congruent: $RW \cong KG$, $WK \cong GR$.
Also, $\overline{RK}$ is a common side to both triangles.

Step2: Apply SSS congruence rule

For $\triangle RWK$ and $\triangle KGR$:

1. $RW \cong KG$ (Opposite sides of parallelogram)
2. $WK \cong GR$ (Opposite sides of parallelogram)
3. $RK \cong KR$ (Reflexive Property of Congruence)

By the Side-Side-Side (SSS) Congruence Postulate, $\triangle RWK \cong \triangle KGR$.

Answer:

$\triangle RWK \cong \triangle KGR$ is proven by the SSS Congruence Postulate, using properties of parallelograms and the reflexive property of congruence.

Two-Column Proof Format:

Statements	Reasons
2. $RW \cong KG$, $WK \cong GR$	2. Opposite sides of a parallelogram are congruent
3. $RK \cong KR$	3. Reflexive Property of Congruence
4. $\triangle RWK \cong \triangle KGR$	4. SSS Congruence Postulate