Question

1. what is the definition of congruence?

the property of two figures having exactly the same shape and same
size.

1. draw the directed line segment translates polygon p to polygon q?

1. which segment is the image of ab when rotated 90° counterclockwise around point p?

fg

1. there is a square abcd, inscribed in a circle with center o. what is the smallest angle

we can rotate around o so that the image of a is b?
90 degrees.

1. what type of triangle has one line of symmetry? isosceles

what type of triangle has three lines of symmetry? equilateral
what type of triangle has no line of symmetry? scalene

1. what is the measure of angle abe? what is the measure of angle abc?

abe= 140
abc=40

Explanation:

Problem 8

Step1: Recall square properties

A square has 4 equal sides and 4 right angles. When inscribed in a circle, the center \( O \) is also the center of the square. The vertices of the square divide the circle into 4 equal arcs.

Step2: Calculate central angle

The total angle around a point (center \( O \)) is \( 360^\circ \). For a square, there are 4 equal arcs between consecutive vertices. So the angle between two consecutive vertices (like \( A \) and \( B \)) is \( \frac{360^\circ}{4}=90^\circ \). So rotating the square \( 90^\circ \) around \( O \) will map \( A \) to \( B \).

Step1: Analyze angle relationships

From the diagram, \( \angle ABC = 40^\circ \) (given as \( 40^\circ \) in the diagram). \( \angle ABE \) and \( \angle ABC \) are supplementary angles (they form a linear pair, so their sum is \( 180^\circ \)).

Step2: Calculate \( \angle ABE \)

Using the supplementary angle formula: \( \angle ABE + \angle ABC = 180^\circ \). Substituting \( \angle ABC = 40^\circ \), we get \( \angle ABE = 180^\circ - 40^\circ = 140^\circ \).

Answer:

\( 90^\circ \)

Problem 10