Math 9 Properties of Parallelograms Properties of

Transcript:Math 9 Properties of Parallelograms Properties of:
Math 9 Properties of Parallelograms Properties of Parallelograms > > parallelogram Opposite sides of a parallelogram are parallel. The opposite angles of a parallelogram are congruent. The opposite sides of a parallelogram are congruent. The consecutive angles of a parallelogram are supplementary. The diagonals of a parallelogram bisect each other. Each diagonal divides a parallelogram into two congruent triangles. > > > > 𝑳 𝑰 𝑬 𝟖𝟔° 𝟐𝟎 𝒄𝒎 Properties of Parallelograms Find: 𝐿𝐸 𝑳𝑬 = 𝟏𝟕 𝐸𝐹 𝑬𝑭 = 𝟐𝟎 𝑚∠𝐿𝐸𝐹 𝟏𝟕 𝒄𝒎 𝒎∠𝑳𝑬𝑭 = 𝟗𝟒° a. b. c. F 𝑚∠𝐿 𝑚∠𝐼 𝑚∠𝐹 𝒎∠𝑳 = 𝟖𝟔° 𝒎∠𝑰 = 𝟗𝟒° 𝒎∠𝑭 = 𝟖𝟔° Special Types of Parallelograms Special Types square > > >> >> > > >> >> rectangle rhombus square > > >> >> > > >> >> rectangle rhombus All properties of parallelograms. It has four right angles. Its diagonals are congruent. Special Types square > > >> >> rhombus > > >> >> rectangle > > > > > > 𝑹 𝑬 𝑻 𝑵 𝑺 1. Find 𝐸𝑇 if 𝑅𝑆 = 13 𝑚. 𝑬𝑻 = 𝟐𝟔 1. Find m∠𝑇𝑅𝑁. 𝒎∠𝑻𝑹𝑵 = 𝟔𝟔° 𝟐𝟒° Special Types square > > >> >> > > >> >> rectangle rhombus Properties inherited from the parallelogram. It has four congruent sides. Its diagonals are perpendicular. Each diagonal bisects the angles of the rhombus. Special Types square > > >> >> > > >> >> rhombus rectangle Given: rhombus 𝑅𝑂𝐴𝐷 If m∠𝑅𝑂𝐴 = 108°, find: m∠𝑅𝑂𝐵 m∠𝑂𝑅𝐵 m∠𝑂𝑅𝐷 𝐦∠𝑹𝑶𝑩 = 𝟓𝟒° 𝐦∠𝑶𝑹𝑩 = 𝟑𝟔° 𝐦∠𝑶𝑹𝑩 = 𝟕𝟐° 𝑩 𝑹 𝑨 𝑶 𝑫 Special Types square > > >> >> > > >> >> rectangle rhombus All properties of a parallelogram. All properties of a rectangle. All properties of a rhombus. Special Types