Table of Contents

## How do you prove ABC is congruent to CDA?

Since the diagonal AC is the same for triangles ABC and CDA we can use **the SSS theorem** to prove that triangle ABC is congruent to triangle CDA (side AB ≅ side CD side AD ≅ side BC and side AC ≅ side AC).

## Why is ABC congruent to CDA?

Summary: Triangle ABC is congruent to triangle CDA and it is **established by the fulfillment of the condition SAS** (two sides and an included angle).

## Why are the triangles in a rhombus congruent?

Proof that **the diagonals of a rhombus are perpendicular**

Corresponding parts of congruent triangles are congruent so all 4 angles (the ones in the middle) are congruent. This leads to the fact that they are all equal to 90 degrees and the diagonals are perpendicular to each other.

## What can you say about ABC and CDA?

**ABC and CDA are congruent**. Two sides and an included angle of triangle ABC are congruent to two corresponding sides and an included angle in triangle CDA. According to the above postulate the two triangles ABC and CDA are congruent.

## What is the measure of angle C triangle ABC is isosceles?

Step-by-step explanation:

180=180. So **60°** is the answer.

## What is a vertical angle in geometry?

Definition of vertical angle

: **either of two angles lying on opposite sides of two intersecting lines**.

## Which shows two triangles are congruent by ASA?

The ASA rule states that: **If two angles and the included side of one triangle are equal to two angles and included side of another triangle** then the triangles are congruent.

## What are triangle proofs?

Explanation: … The Side-Angle-Side Theorem (SAS) states that if two sides and the angle between those two sides of a triangle are equal to two sides and the angle between those sides of another triangle then these two triangles are congruent.

## How do you show ABCD is a rhombus?

Show that **if the diagonals of a quadrilateral bisect each other at right angles** then it is a rhombus. Sol: We have a quadrilateral ABCD such that the diagonals AC and BD bisect each other at right angles at O. Their corresponding parts are equal. Thus the quadrilateral ABCD is a rhombus.

## How do you prove ABCD is a rhombus?

Prove that when in **a rectangle** the midpoints of the sides of the rectangle are drawn and labeled A B C and D then the quadrilateral ABCD is a rhombus. Say that the rectangle had side lengths of length e and f. Then the side lengths of quadrilateral ABCD by the Pythagorean Theorem are √(e2)2+(f2)2.

## What is the theorem of rhombus?

THEOREM: **If a parallelogram is a rhombus each diagonal bisects a pair of opposite angles**. THEOREM Converse: If a parallelogram has diagonals that bisect a pair of opposite angles it is a rhombus. THEOREM: If a parallelogram is a rhombus the diagonals are perpendicular.

## What is the ASA theorem?

**if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle then the two triangles are congruent**.

## What’s SSS in geometry?

**side-side-side**) All three corresponding sides are congruent. SAS (side-angle-side) Two sides and the angle between them are congruent.

## We can then determine △ABC ≅ △AED by . Because of CPCTC segment AC is congruent to segment . Triangle ACD is an isosceles triangle based on the definition of isosceles triangle. Therefore based on the **isosceles triangle theorem** ∠ACD ≅ ∠ADC.
## Is triangle ABC an isosceles?

Thus given two equal sides and a single angle the entire structure of the triangle can be determined. …

## What is the M ∠ ABC?

Measure of an angle

When we say ‘the angle ABC’ we mean **the actual angle object**. If we want to talk about the size or measure of the angle in degrees we should say ‘the measure of the angle ABC’ – often written m∠ABC.

## What is angle measure in C?

To find angle C we simply plug into the formula above and solve for C. To check if 80 degrees is correct let’s add all three angle measures. If we get **180 degrees** then our answer for angle C is right. 180 = 180…
## Why are vertical angles called vertical?

‘Vertical’ has come to mean ‘upright’ or the opposite of horizontal. But here it has more to do with the word ‘vertex’. Vertical angles are called that **because they share a common vertex.**

## What is the vertical?

A vertical is **an alignment in which the top is always above the bottom**. It is a property of two or more points in which if a point is directly below the second point and they are vertical to each other. … Vertical lines or objects are always perpendicular to the horizontal lines or objects.

## Why are vertical angles equal?

When two straight lines intersect each other vertical angles are formed. **Vertical angles are always congruent and equal**. Vertical angles are congruent as the two pairs of non-adjacent angles formed by intersecting two lines superimpose on each other.
## Which postulate or theorem proves that △ ABC and △ CDA are congruent?

Which postulate or theorem proves that △ABC and △CDA are congruent? **ASA Congruence Postulate**.
## Which congruence theorem can be used to prove ABC is congruent to DEC?

Vertical Angles Congruence Theorem
You can use **the Vertical Angles Congruence Theorem** to prove that ABC ≅ DEC. b. ∠CAB ≅ ∠CDE because corresponding parts of congruent triangles are congruent.
## What additional information is needed to show that △ ABC ≅ △ def by Asa?

△ABC ≅ △DEF. **If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle then the two triangles are congruent**. Use the ASA and AAS Congruence Theorems.

## What is angle addition?

The angle addition postulate states that if B is in the interior of A O C then. **m ∠ A O B + m ∠ B O C = m ∠ A O C**. That is the measure of the larger angle is the sum of the measures of the two smaller ones.
## What are corresponding angles?

Definition: Corresponding angles are **the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line** (i.e. the transversal). For example in the below-given figure angle p and angle w are the corresponding angles.
## What is SSS SAS ASA AAS?

SSS (**Side-Side-Side**) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side) RHS (Right angle-Hypotenuse-Side)

## How do you prove ABCD is a quadrilateral?

**ABCD is a quadrilateral in which AB = CD and AB || CD .**
- To prove :
- Construction : Joined AC.
- Solution: In △s ABC and CDA we have. AB = CD [Given] AC = AC [Common] and ∠BAC = ∠DCA. …
- 9.5. MIDPOINT THEOREM.
- Given : ABC is a triangle in which D and E are the mid-points of sides AB and AC respectively DE is joined.

## How do you prove that ABCD is a rectangle?

– The diagonals are congruent. Let’s see why we can claim that the diagonals are congruent. Here is a sample proof: Given: Quadrilateral ABCD is a rectangle.

…

Prove it is a Rectangle.
Statements
Reasons
Definition of Rectangle
ΔBCD ≅ ΔADC
Side Angle Side
AC ≅ BD
CPCTC

## What information can be used to prove parallelogram ABCD is also a rhombus?

**If two consecutive sides of a parallelogram are congruent** then it’s a rhombus (neither the reverse of the definition nor the converse of a property). If either diagonal of a parallelogram bisects two angles then it’s a rhombus (neither the reverse of the definition nor the converse of a property).

## Is parallelogram ABCD a rhombus?

Because AB ~= BC and AB ~= BC are adjacent sides you have a **parallelogram with congruent adjacent sides** a.k.a. a rhombus.

…

Geometry.
Statements
Reasons
9.
Parallelogram ABCD is a rhombus
Definition of rhombus

## What makes a rhombus a rhombus?

In plane Euclidean geometry a rhombus (plural rhombi or rhombuses) is a **quadrilateral whose four sides all have the same length**. … Every rhombus is simple (non-self-intersecting) and is a special case of a parallelogram and a kite. A rhombus with right angles is a square.
## What are the 4 properties of a rhombus?

**A rhombus is a quadrilateral that has the following four properties:**
- Opposite angles are equal.
- All sides are equal and opposite sides are parallel to each other.
- Diagonals bisect each other perpendicularly.
- Sum of any two adjacent angles is 180°

## What theorem or postulate is used to prove ABCD is a parallelogram?

Theorem: **The diagonals of a parallelogram bisect each other**. Proof: Given ABCD let the diagonals AC and BD intersect at E we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram.

## Which theorem can be used to prove that the quadrilateral ABCD is a parallelogram?

If — AB ≅ — CD and — BC ≅ — DA then ABCD is a parallelogram. **If both pairs of opposite angles of a quadrilateral are congruent** then the quadrilateral is a parallelogram.

## ABCD is a rhombus with `/_ABC = 56^(@)` then `/_ACD` is equal to:

## ABCD is a rhombus such that `angle ACB = 50^(@). ” Then. ” angle ADB=` ?

## ABCD is a rhombus such that `angle ACB=40^(@). ” Find ” angle ADB.`

## In the adjoining figure ABCD is a rhombus. If `/_A=70^@` then `/_CDB=?`

“

**the actual angle object**. If we want to talk about the size or measure of the angle in degrees we should say ‘the measure of the angle ABC’ – often written m∠ABC.

**180 degrees**then our answer for angle C is right. 180 = 180…

## Why are vertical angles called vertical?

‘Vertical’ has come to mean ‘upright’ or the opposite of horizontal. But here it has more to do with the word ‘vertex’. Vertical angles are called that **because they share a common vertex.**

## What is the vertical?

A vertical is **an alignment in which the top is always above the bottom**. It is a property of two or more points in which if a point is directly below the second point and they are vertical to each other. … Vertical lines or objects are always perpendicular to the horizontal lines or objects.

## Why are vertical angles equal?

**Vertical angles are always congruent and equal**. Vertical angles are congruent as the two pairs of non-adjacent angles formed by intersecting two lines superimpose on each other.

## Which postulate or theorem proves that △ ABC and △ CDA are congruent?

**ASA Congruence Postulate**.

## Which congruence theorem can be used to prove ABC is congruent to DEC?

**the Vertical Angles Congruence Theorem**to prove that ABC ≅ DEC. b. ∠CAB ≅ ∠CDE because corresponding parts of congruent triangles are congruent.

## What additional information is needed to show that △ ABC ≅ △ def by Asa?

△ABC ≅ △DEF. **If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle then the two triangles are congruent**. Use the ASA and AAS Congruence Theorems.

## What is angle addition?

**m ∠ A O B + m ∠ B O C = m ∠ A O C**. That is the measure of the larger angle is the sum of the measures of the two smaller ones.

## What are corresponding angles?

**the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line**(i.e. the transversal). For example in the below-given figure angle p and angle w are the corresponding angles.

## What is SSS SAS ASA AAS?

SSS (**Side-Side-Side**) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side) RHS (Right angle-Hypotenuse-Side)

## How do you prove ABCD is a quadrilateral?

**ABCD is a quadrilateral in which AB = CD and AB || CD .**

- To prove :
- Construction : Joined AC.
- Solution: In △s ABC and CDA we have. AB = CD [Given] AC = AC [Common] and ∠BAC = ∠DCA. …
- 9.5. MIDPOINT THEOREM.
- Given : ABC is a triangle in which D and E are the mid-points of sides AB and AC respectively DE is joined.

## How do you prove that ABCD is a rectangle?

…

Prove it is a Rectangle.

Statements | Reasons |
---|---|

Definition of Rectangle | |

ΔBCD ≅ ΔADC | Side Angle Side |

AC ≅ BD | CPCTC |

## What information can be used to prove parallelogram ABCD is also a rhombus?

**If two consecutive sides of a parallelogram are congruent** then it’s a rhombus (neither the reverse of the definition nor the converse of a property). If either diagonal of a parallelogram bisects two angles then it’s a rhombus (neither the reverse of the definition nor the converse of a property).

## Is parallelogram ABCD a rhombus?

**parallelogram with congruent adjacent sides**a.k.a. a rhombus.

…

Geometry.

Statements | Reasons | |
---|---|---|

9. | Parallelogram ABCD is a rhombus | Definition of rhombus |

## What makes a rhombus a rhombus?

**quadrilateral whose four sides all have the same length**. … Every rhombus is simple (non-self-intersecting) and is a special case of a parallelogram and a kite. A rhombus with right angles is a square.

## What are the 4 properties of a rhombus?

**A rhombus is a quadrilateral that has the following four properties:**

- Opposite angles are equal.
- All sides are equal and opposite sides are parallel to each other.
- Diagonals bisect each other perpendicularly.
- Sum of any two adjacent angles is 180°

## What theorem or postulate is used to prove ABCD is a parallelogram?

Theorem: **The diagonals of a parallelogram bisect each other**. Proof: Given ABCD let the diagonals AC and BD intersect at E we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram.

## Which theorem can be used to prove that the quadrilateral ABCD is a parallelogram?

If — AB ≅ — CD and — BC ≅ — DA then ABCD is a parallelogram. **If both pairs of opposite angles of a quadrilateral are congruent** then the quadrilateral is a parallelogram.

## ABCD is a rhombus with `/_ABC = 56^(@)` then `/_ACD` is equal to:

## ABCD is a rhombus such that `angle ACB = 50^(@). ” Then. ” angle ADB=` ?

## ABCD is a rhombus such that `angle ACB=40^(@). ” Find ” angle ADB.`

## In the adjoining figure ABCD is a rhombus. If `/_A=70^@` then `/_CDB=?`

“