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Q: What has 4 equal angles and 2 pairs of matching sides and two lines of symmetry?

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An irregular pentagon such as a child's silhouette of a house: a rectangle shape (open at the top) forming the body of the house, with a triangular roof on of the rectangle. The vertical line through the apex of the roof is the line of symmetry. The two walls, and the two roof lines are the two sets of equal sides. The two right angles at the base are the one set of matching angles.

triangle

Pentagon

An equilateral triangle has 3 equal acute angles of 60 degrees and it has 3 lines of symmetry.

An irregular quadrilateral.

Related questions

corresponding and alternate angles

An irregular pentagon such as a child's silhouette of a house: a rectangle shape (open at the top) forming the body of the house, with a triangular roof on of the rectangle. The vertical line through the apex of the roof is the line of symmetry. The two walls, and the two roof lines are the two sets of equal sides. The two right angles at the base are the one set of matching angles.

hsa

Parallelogram

star

triangle

Pentagon

an equilateral triangle

octagon

Impossible.

Square

If your asking what shape has three lines of symmetry, your answer would be an equilateral triangle. You can tell how many lines of symmetry a shape that has all angles of the same measure has by looking at it's angles. Ex., pentagon has five angles--five lines of symmetry; octagon has eight angles, eight lines of symmetry; etc.