Using Congruent Triangles

ABCD is a Rhombus. What is the definition of a rhombus?

• A quadrilateral in which the opposite sides are parallel

• A quadrilateral with 4 right angles

• A quadrilateral with 4 congruent sides

• A quadrilateral with 4 right angles and 4 congruent sides

Tags

CCSS.HSG.CO.C.11

ABCD is a Rhombus. If you want to prove that Diagonal BD is a line of symmetry, what 2 triangles need to be congruent?

• △ABC ≅ △ADC

• △BAD ≅ △BCD

• △ABC ≅ △BCD

• △BAD ≅ △ADC

ABCD is a Rhombus. If you want to prove that opposite angles ∠B and ∠D are congruent, what 2 triangles need to be congruent?

• △ABC ≅ △ADC

• △BAD ≅ △BCD

• △ABC ≅ △BCD

• △BAD ≅ △ADC

Tags

CCSS.HSG.SRT.B.5

ABCD is a Rhombus. How could you transform △BAD so that it is on △BCD?

• Translate △BAD to the right so Point A lines up with Point C

• Rotate △BAD 180° around Point B

• Rotate △BAD 90° clockwise around Point D

• Reflect △BAD across Line Segment BD

Tags

CCSS.8.G.A.3

Based on the definition of a rhombus, what triangle criteria proves that △BAD ≅ △BCD?

• 3 Congruent Angles (AAA)

• 3 Congruent Sides (SSS)

• 2 Sides and an Included Angle (SAS)

• 2 Angles and an Included Side (ASA)

Tags

CCSS.HSG.SRT.B.5

If we know △BAD ≅ △BCD, what math postulate (rule) proves that ∠A≅∠C?

• 3 Congruent Angles (AAA)

• 2 Angles and an Included Side are Congruent (ASA)

• Corresponding Parts of Congruent Triangles are Congruent

• Corresponding Angles of Similar Figures are Congruent

Tags

CCSS.HSG.SRT.B.5

ABCD is a Rectangle. What is the definition of a rectangle?

• A quadrilateral in which the opposite sides are parallel

• A quadrilateral with 4 right angles

• A quadrilateral with 4 congruent sides

• A quadrilateral with 4 right angles and 4 congruent sides

Tags

CCSS.3.G.A.1

ABCD is a rectangle. How could you transform △BAD so that it is on △DCB?

• Translate △BAD so Point A lines up with Point C

• Rotate △BAD 180° around the midpoint of diagonal BD

• Rotate △BAD 90° clockwise around the midpoint of diagonal BD

• Reflect △BAD across Line diagonal BD

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

ABCD is a rectangle. What triangle criteria proves that △BAD ≅ △DCB? Select all that apply.

• 3 Congruent Angles (AAA)

• 3 Congruent Sides (SSS)

• 2 Sides and an Included Angle (SAS)

• 2 Angles and an Included Side (ASA)

• Hypotenuse and a Leg (HL)

Tags

CCSS.HSG.SRT.B.5

In rectangle ABCD, we know you can draw diagonal BD to make the pair of congruent triangles △BAD and △DCB. Can you make any other pairs of congruent triangles within the rectangle? Explain how and what the triangles would be.

Tags

CCSS.HSG.CO.C.11