Congruent Triangles 1
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Question 1 of 4
1. Question
Is `∆XYU` congruent to `∆ZUW`
Hint
Help VideoCorrect
Well Done!
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Two triangles are congruent if all corresponding angles and sides are equalUse the given diagram to determine whether any of the angles or sides are congruentStatement: `XU``=``UW`Reason: Given by the markings (two dashes) on each segment`(S)` Side
Statement: `/_ XUY``=``/_ ZUW`Reason: Vertically Opposite angles are equal`(A)` Angle
We have proved congruence of `1` side and `2` angles between the two triangles. Therefore, the two triangles are congruent according to the Angle-Angle-Side `\text((AAS))` criteriaYes, `∆XYU` is congruent to `∆ZUW`More InfoCongruent TrianglesUse any of the following 4 tests to prove congruence between two triangles:Side-Side-Side `\text((SSS))`
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.
Side-Angle-Side `\text((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 `\text((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 `\text((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 TypesAlternate 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°.` These angles typically form a C Shape
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Question 2 of 4
2. Question
Is `∆XYW` congruent to `∆YZW`
Hint
Help VideoCorrect
Nice Job!
Incorrect
Two triangles are congruent if all corresponding angles and sides are equalUse the given diagram to determine whether any of the angles or sides are congruentStatement: `XY``=``YZ`Reason: Given by the markings (two dashes) on each segment`(S)` Side
Statement: `XW``=``WZ`Reason: Given by the markings (one dash) on each segment`(S)` Side
Statement: `YW``=``YW`Reason: This is a common side for both triangles`(S)` Side
We have proved congruence of `3` sides angles between the two triangles. Therefore, the two triangles are congruent according to the Side-Side-Side `\text((SSS))` criteriaYes, `∆XYW` is congruent to `∆YZW`More InfoCongruent TrianglesUse any of the following 4 tests to prove congruence between two triangles:Side-Side-Side `\text((SSS))`
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.Side-Angle-Side `\text((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 otherAngle-Angle-Side `\text((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 `\text((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 anotherAlternate, Corresponding and Co-Interior Angle TypesAlternate 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°.` These angles typically form a C Shape -
Question 3 of 4
3. Question
Is `∆AED` congruent to `∆EBC`
Hint
Help VideoCorrect
Excellent!
Incorrect
Two triangles are congruent if all corresponding angles and sides are equalUse the given diagram to determine whether any of the angles or sides are congruentStatement: `AE``=``EC`Reason: Given by the markings (two dashes) on each segment`(S)` Side
Statement: `/_ AED``=``/_ BEC`Reason: Vertically Opposite angles are equal`(A)` Angle
Statement: `DE``=``EB`Reason: Given by the markings (one dash) on each segment`(S)` Side
We have proved congruence of `2` sides and `1` angle between the two triangles. Therefore, the two triangles are congruent according to the Side-Angle-Side `\text((SAS))` criteriaYes, `∆AED` is congruent to `∆EBC`More InfoCongruent TrianglesUse any of the following 4 tests to prove congruence between two triangles:Side-Side-Side `\text((SSS))`
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.Side-Angle-Side `\text((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 otherAngle-Angle-Side `\text((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 `\text((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 anotherAlternate, Corresponding and Co-Interior Angle TypesAlternate 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°.` These angles typically form a C Shape -
Question 4 of 4
4. Question
Is side `BC` equal to side `EF`
Hint
Help VideoCorrect
Fantastic!
Incorrect
Two triangles are congruent if all corresponding angles and sides are equalUse the given diagram to determine whether any of the angles or sides are congruentStatement: `/_ A``=``/_ D`Reason: Given by the values (`55°`) on each segment`(A)` Angle
Statement: `/_ C``=``/_ F`Reason: Given by the values (`65°`) on each segment`(A)` Angle
Statement: `AB``=``ED`Reason: Given by the markings (one dash) on each segment`(S)` Side
We have proved congruence of `2` angles and `1` side between the two triangles. Therefore, the two triangles are congruent according to the Angle-Angle-Side `\text((AAS))` criteriaSince we have proven the congruence of the two triangles, it means that corresponding sides, such as sides `BC` and `EF`, are equal.Yes, side `BC` is equal to side `EF`More InfoCongruent TrianglesUse any of the following 4 tests to prove congruence between two triangles:Side-Side-Side `\text((SSS))`
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.Side-Angle-Side `\text((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 otherAngle-Angle-Side `\text((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 `\text((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 anotherAlternate, Corresponding and Co-Interior Angle TypesAlternate 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°.` These angles typically form a C Shape