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What is necessary when proving that the diagonals of a rectangle are congruent?
opposite sides are congruent corresponding parts of congruent triangles are congruent(apex)
What is necessary when proving that the opposite sides of a parallelogram are congruent?
1. Opposite sides are parallel 2. Corresponding parts of congruent triangles are congruent
Are necessary when proving that the opposite angles of a parallelogram are congruent?
A basic knowledge of angles when two parallel lines meet a transversal is necessary.
What are necessary when proving that the opposite sides of a parallelogram are congruent?
A. Corresponding parts of similar triangles are similar.B. Alternate interior angles are supplementary.C. Alternate interior angles are congruent.D. Corresponding parts of congruent triangles are congruent
Why do you think that diagonals bisect each other for proving that a quadrilateral is a parallelogram?
The diagonals divide the quadrilateral into four sections. You can then use the bisection to prove that opposite triangles are congruent (SAS). That can then enable you to show that the alternate angles at the ends of the diagonal are equal and that shows one pair of sides is parallel. Repeat the process with the other pair of triangles to show that the second pair of sides is parallel. A quadrilateral with two pairs of parallel lines is a parallelogram.
What is necessary when proving that the diagonals of a rectangle are congruent?
opposite sides are congruent corresponding parts of congruent triangles are congruent(apex)
Is a rhombus always sometimes or never a parallelogram?
Always. In fact, one method of proving a quadrilateral a rhombus is by first proving it a parallelogram, and then proving two consecutive sides congruent, diagonals bisecting verticies, etc.
What is necessary when proving that the opposite sides of a parallelogram are congruent?
1. Opposite sides are parallel 2. Corresponding parts of congruent triangles are congruent
Are necessary when proving that the opposite angles of a parallelogram are congruent?
A basic knowledge of angles when two parallel lines meet a transversal is necessary.
Why is drawing the diagonals of a parallelogram help full in proving many of the parallelograms properties?
It is helpful (not help full) because the two triangles formed by either diagonal are congruent.
What is special about the diagonals of a parallelogram?
In a parallelogram, the diagonals bisect each other, meaning they cut each other exactly in half at their intersection point. Additionally, while the diagonals are not necessarily equal in length, they do divide the parallelogram into two congruent triangles. This property is fundamental in proving various characteristics of parallelograms and is essential in geometry.
What is necessary when proving that the opposite angles of a parallelogram are congruent?
Because its 4 interior angles must add up to 360 degrees
What are necessary when proving that the oppsite sides of a parallelogram are congruent check all that apply?
To prove that the opposite sides of a parallelogram are congruent, you need to establish that the shape is a parallelogram, which can be done by showing that either pairs of opposite sides are parallel (using the properties of parallel lines) or that the diagonals bisect each other. Additionally, applying the properties of congruent triangles (such as using the Side-Side-Side or Side-Angle-Side postulates) can further support the proof. Ensure to use clear definitions and properties of parallelograms throughout the proof.
What are necessary when proving that the opposite sides of a parallelogram are congruent?
A. Corresponding parts of similar triangles are similar.B. Alternate interior angles are supplementary.C. Alternate interior angles are congruent.D. Corresponding parts of congruent triangles are congruent
How can proving two triangles congruent can help prove parts of the triangle congruent?
When you prove a triangle is congruent to another, it can help you prove parts of the triangle congruent by checking the ratio between all sides and angles. Thank you for asking
What method proves a trapezoid isosceles?
A trapezoid can be proven isosceles by proving that the 2 legs are congruent (by definition), or that the 2 base angles (either upper or lower) are congruent.
Why do you think that diagonals bisect each other for proving that a quadrilateral is a parallelogram?
The diagonals divide the quadrilateral into four sections. You can then use the bisection to prove that opposite triangles are congruent (SAS). That can then enable you to show that the alternate angles at the ends of the diagonal are equal and that shows one pair of sides is parallel. Repeat the process with the other pair of triangles to show that the second pair of sides is parallel. A quadrilateral with two pairs of parallel lines is a parallelogram.
