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If two triangles have a congruent angle and two congruent sides then are the triangles guaranteed to be congruent?
Only if the congruent angle is the angle between the two congruent sides (SAS postulate).
Do all parallelograms have diagonals which bisect?
Yes; all parallelograms have diagonals that bisect each other. Other properties of parallelograms are: * The opposite sides are congruent. * The opposite sides are parallel. * The opposite angles are congruent.
Which quadrilaterals always have 2 pairs of parallel sides and always have 4 congruent angle?
Square and rectangle.
What is one way to prove that a quadrilateral is a parallegram?
* both pairs of opposite sides are parallel * both pairs of opposite sides are congruent * both pairs of opposite angles are congruent * one pair of opposite sides are parallel and congruent * both diagonals bisect each other * all consecutive angle pairs are supplementary
What are reasons used in the proof that the angle bisector construction can be used to bisect any angle?
The angle bisector construction can bisect any angle due to the properties of congruent triangles and the equal distances from a point on the bisector to the sides of the angle. By drawing an arc from the vertex that intersects both sides, we create two segments that can be shown to be equal. Using the triangle congruence criteria (such as the Side-Angle-Side or Angle-Side-Angle postulates), we can demonstrate that the angles formed are congruent, confirming that the angle has been bisected accurately. Thus, any angle can be bisected using this construction method.
What are 4 different types of quadrilateralas?
There are: Squares, which have all four sides parallel and congruent, all four angles are right and congruent, the diagonals bisect each other and are congruent. Trapezoids, which have two of their sides parallel Rhombus, which have all sides congruent, diagonals bisect, and opposite angles are congruent Parallelograms, which have opposite sides congruent and parallel, diagonals bisect Rectangle, which is a square but one pair of opposite sides aren't congruent.
If two triangles have a congruent angle and two congruent sides then are the triangles guaranteed to be congruent?
Only if the congruent angle is the angle between the two congruent sides (SAS postulate).
Do all parallelograms have diagonals which bisect?
Yes; all parallelograms have diagonals that bisect each other. Other properties of parallelograms are: * The opposite sides are congruent. * The opposite sides are parallel. * The opposite angles are congruent.
What are the 5 properties of parallelograms?
If one angle is right, then all angles are right. The diagonals of a parallelogram bisect each other. Opposite angles are congruent. Opposite sides are congruent. Consecutive angles are supplementary.
Which quadrilaterals always have 2 pairs of parallel sides and always have 4 congruent angle?
Square and rectangle.
What is one way to prove that a quadrilateral is a parallegram?
* both pairs of opposite sides are parallel * both pairs of opposite sides are congruent * both pairs of opposite angles are congruent * one pair of opposite sides are parallel and congruent * both diagonals bisect each other * all consecutive angle pairs are supplementary
What shape has 2 congruent diagonals that do not bisect?
A trapezoid Trapezoid - 2 congruent diagonals that do not bisect each other. No right angles and has 1 pair of opposite parallel sides.
What are reasons used in the proof that the angle bisector construction can be used to bisect any angle?
The angle bisector construction can bisect any angle due to the properties of congruent triangles and the equal distances from a point on the bisector to the sides of the angle. By drawing an arc from the vertex that intersects both sides, we create two segments that can be shown to be equal. Using the triangle congruence criteria (such as the Side-Angle-Side or Angle-Side-Angle postulates), we can demonstrate that the angles formed are congruent, confirming that the angle has been bisected accurately. Thus, any angle can be bisected using this construction method.
If two sides of a rectangle are congruent then then angles oppposite those sides are always congruent?
No "if" is necessary in this case. All angles of a rectangle are congruent, by definition. Also, there is no "angle opposite a side" in a rectangle.
In a rectangle will the diagonals always bisect opposite sides?
Diagonals never bisect sides. They join the ends of sides.In a rectangle, the diagonals always bisect each other.
What type of angle has one angle greater than 90 degrees and two sides that are congruent?
None, because an angle cannot have congruent sides.
What is the angle-angle-side rule?
Side-Angle-Side is a rule used in geometry to prove triangles congruent. The rule states that if two sides and the included angle are congruent to two sides and the included angle of a second triangle, the two triangles are congruent. An included angle is an angle created by two sides of a triangle.
