Q. What do all Rhombuses have in common?
Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides. Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties: Opposite angles of a rhombus have equal measure.
Q. Are two Rhombuses with the same side lengths always congruent?
Two rhombuses with the same side lengths are always congruent. Two parallelograms with the same side lengths are always congruent.
Table of Contents
- Q. What do all Rhombuses have in common?
- Q. Are two Rhombuses with the same side lengths always congruent?
- Q. Are all sides of a parallelogram are congruent?
- Q. Do two rectangles always have the same shape?
- Q. How can you tell if two figures are similar?
- Q. Which condition justifies why all squares are similar?
- Q. Why is the AAA similarity test not necessary?
- Q. Is Asa a similarity theorem?
- Q. Is Asa a congruence theorem?
- Q. Is SSA a postulate?
- Q. Is SSA a valid criterion?
- Q. What does AAS look like?
Q. Are all sides of a parallelogram are congruent?
If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Q. Do two rectangles always have the same shape?
No they are not; rectangles are only similar if there is a consistent ratio between all sides. An example of two rectangles that are similar would be a rectangle with dimensions of 2 x 7 and another one with dimensions of 4 x 14.
Q. How can you tell if two figures are similar?
Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor .
Q. Which condition justifies why all squares are similar?
Q. Which condition justifies why all squares are similar? Corresponding angles are congruent and all sides are proportional. All squares have congruent angles and sides.
Q. Why is the AAA similarity test not necessary?
Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles. We said if you know that 3 sides of one triangle are congruent to 3 sides of another triangle, they have to be congruent. The same is true for side angle side, angle side angle and angle angle side.
Q. Is Asa a similarity theorem?
For the configurations known as angle-angle-side (AAS), angle-side-angle (ASA) or side-angle-angle (SAA), it doesn’t matter how big the sides are; the triangles will always be similar. These configurations reduce to the angle-angle AA theorem, which means all three angles are the same and the triangles are similar.
Q. Is Asa a congruence theorem?
ASA Theorem (Angle-Side-Angle) The Angle Side Angle Postulate (ASA) says triangles are congruent if any two angles and their included side are equal in the triangles. An included side is the side between two angles. The postulate says you can pick any two angles and their included side.
Q. Is SSA a postulate?
There are some cases when SSA can imply triangle congruence, but not always. This is why it’s not like the other triangle congruence postulates/criteria.
Q. Is SSA a valid criterion?
In other words, congruence through SSA is invalid. A pair of sides and the included angle will uniquely determine a triangle. In other words, congruence through SAS is valid.
Q. What does AAS look like?
AAS stands for “angle, angle, side” and means that we have two triangles where we know two angles and the non-included side are equal. If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
