We have proved congruence of 11 side and 22 angles between the two triangles. Therefore, the two triangles are congruent according to the Angle-Angle-Side (AAS)(AAS) criteria
Yes, ∆XYUΔXYU is congruent to ∆ZUWΔZUW
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Congruent Triangles
Use any of the following 4 tests to prove congruence between two triangles:
Side-Side-Side (SSS)(SSS)
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.
Side-Angle-Side (SAS)(SAS)
Two triangles are congruent if 2 sides and the included angle of one are respectively equal to 2 sides and the included angle of the other
Angle-Angle-Side (AAS)(AAS)
Two triangles are congruent if 2 angles and a side of one are respectively equal to 2 angles and the corresponding side of the other.
Right Angle-Hypotenuse-Side (RHS)(RHS)
Two right angled triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of another
Alternate, Corresponding and Co-Interior Angle Types
Alternate Angles
Alternate Angles in parallel lines are equal. These angles typically form a Z shape.
Corresponding Angles
Corresponding Angles in parallel lines are equal. These angles typically form an F shape.
Co-Interior Angles
Co-Interior Angles are when two angles have a sum of 180°.180°. These angles typically form a C Shape
Use the given diagram to determine whether any of the angles or sides are congruent
Statement: XYXY==YZYZ
Reason: Given by the markings (two dashes) on each segment
(S)(S) Side
Statement: XWXW==WZWZ
Reason: Given by the markings (one dash) on each segment
(S)(S) Side
Statement: YWYW==YWYW
Reason: This is a common side for both triangles
(S)(S) Side
We have proved congruence of 33 sides angles between the two triangles. Therefore, the two triangles are congruent according to the Side-Side-Side (SSS)(SSS) criteria
Yes, ∆XYWΔXYW is congruent to ∆YZWΔYZW
More Info
Congruent Triangles
Use any of the following 4 tests to prove congruence between two triangles:
Side-Side-Side (SSS)(SSS)
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.
Side-Angle-Side (SAS)(SAS)
Two triangles are congruent if 2 sides and the included angle of one are respectively equal to 2 sides and the included angle of the other
Angle-Angle-Side (AAS)(AAS)
Two triangles are congruent if 2 angles and a side of one are respectively equal to 2 angles and the corresponding side of the other.
Right Angle-Hypotenuse-Side (RHS)(RHS)
Two right angled triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of another
Alternate, Corresponding and Co-Interior Angle Types
Alternate Angles
Alternate Angles in parallel lines are equal. These angles typically form a Z shape.
Corresponding Angles
Corresponding Angles in parallel lines are equal. These angles typically form an F shape.
Co-Interior Angles
Co-Interior Angles are when two angles have a sum of 180°.180°. These angles typically form a C Shape
Use the given diagram to determine whether any of the angles or sides are congruent
Statement: AEAE==ECEC
Reason: Given by the markings (two dashes) on each segment
(S)(S) Side
Statement: ∠AED∠AED==∠BEC∠BEC
Reason: Vertically Opposite angles are equal
(A)(A) Angle
Statement: DEDE==EBEB
Reason: Given by the markings (one dash) on each segment
(S)(S) Side
We have proved congruence of 22 sides and 11 angle between the two triangles. Therefore, the two triangles are congruent according to the Side-Angle-Side (SAS)(SAS) criteria
Yes, ∆AEDΔAED is congruent to ∆EBCΔEBC
More Info
Congruent Triangles
Use any of the following 4 tests to prove congruence between two triangles:
Side-Side-Side (SSS)(SSS)
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.
Side-Angle-Side (SAS)(SAS)
Two triangles are congruent if 2 sides and the included angle of one are respectively equal to 2 sides and the included angle of the other
Angle-Angle-Side (AAS)(AAS)
Two triangles are congruent if 2 angles and a side of one are respectively equal to 2 angles and the corresponding side of the other.
Right Angle-Hypotenuse-Side (RHS)(RHS)
Two right angled triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of another
Alternate, Corresponding and Co-Interior Angle Types
Alternate Angles
Alternate Angles in parallel lines are equal. These angles typically form a Z shape.
Corresponding Angles
Corresponding Angles in parallel lines are equal. These angles typically form an F shape.
Co-Interior Angles
Co-Interior Angles are when two angles have a sum of 180°.180°. These angles typically form a C Shape
Use the given diagram to determine whether any of the angles or sides are congruent
Statement: ∠A∠A==∠D∠D
Reason: Given by the values (55°55°) on each segment
(A)(A) Angle
Statement: ∠C∠C==∠F∠F
Reason: Given by the values (65°65°) on each segment
(A)(A) Angle
Statement: ABAB==EDED
Reason: Given by the markings (one dash) on each segment
(S)(S) Side
We have proved congruence of 22 angles and 11 side between the two triangles. Therefore, the two triangles are congruent according to the Angle-Angle-Side (AAS)(AAS) criteria
Since we have proven the congruence of the two triangles, it means that corresponding sides, such as sides BCBC and EFEF, are equal.
Yes, side BCBC is equal to side EFEF
More Info
Congruent Triangles
Use any of the following 4 tests to prove congruence between two triangles:
Side-Side-Side (SSS)(SSS)
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.
Side-Angle-Side (SAS)(SAS)
Two triangles are congruent if 2 sides and the included angle of one are respectively equal to 2 sides and the included angle of the other
Angle-Angle-Side (AAS)(AAS)
Two triangles are congruent if 2 angles and a side of one are respectively equal to 2 angles and the corresponding side of the other.
Right Angle-Hypotenuse-Side (RHS)(RHS)
Two right angled triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of another
Alternate, Corresponding and Co-Interior Angle Types
Alternate Angles
Alternate Angles in parallel lines are equal. These angles typically form a Z shape.
Corresponding Angles
Corresponding Angles in parallel lines are equal. These angles typically form an F shape.
Co-Interior Angles
Co-Interior Angles are when two angles have a sum of 180°.180°. These angles typically form a C Shape