Edna Quirino - SEMESTER 1 STUDY GUIDE Geometry PDF

## SEMESTER 1 STUDY GUIDE ### Find the missing side of each triangle. - 13, 12, _x_ ### What type of transformation was performed below? - The image shows a pair of shapes that are congruent and oriented in opposite directions. It is a **reflection**. ### The equation of the following line is...

## SEMESTER 1 STUDY GUIDE ### Find the missing side of each triangle. - 13, 12, _x_ ### What type of transformation was performed below? - The image shows a pair of shapes that are congruent and oriented in opposite directions. It is a **reflection**. ### The equation of the following line is: y = -x + 4 - Rotate the line 90 degrees clockwise about the origin (0, 0) * What is the y-coordinate of the y-intercept of the new line? [a] **4** * What is the slope of the new line? [b] **1** * What is the relationship between the original and the rotated line? [c] **The lines are perpendicular.** ### The equation of the following line is: y = 1/2x - 3 - Translate the line 5 units up. * What is the y-coordinate of the y-intercept of the new line? [a] **2** * What is the slope of the new line? [b] **1/2** * What is the relationship between the original and the translated line? [c] **The lines are parallel** ### Examine the geometric figure below: - Does it have reflection symmetry? [a] **Yes** - Does it have rotation symmetry other than 360 degrees? [b] **Yes** - Does it have translation symmetry? [c] **No** ### Examine the diagram above and determine the following: - **(2x + 1)°** and **61°** * The angle relationship is [a] **supplementary** * The value of *x* is equal to [b] **20** * The measure of the missing angle is [c] **119°** ### Find the measure of angle *b*. - **48°** and *b* are **supplementary** angles, so their measures add up to 180°. * *b* = 180° - 48° = **132°** ### Examine the diagram above and determine the following: - **15x - 5**, **70°** * The angle relationship is [a] **corresponding** * The value of *x* is equal to [b] **6** * The measure of the angle in bold is [c] **85°** ### Examine the diagram above and determine the following: - **11x + 6**, **12x - 4** * The angle relationship is [a] **supplementary** * The value of *x* is equal to [b] **10** * The measure of the angle in bold is [c] **116°** ### Find the measure of each angle indicated: - **64°**, **36°**, **?** * The angles on the inside of triangle *TJS* add up to 180° * **?** = 180° - 64° - 36° = **80°** ### Calculate the value of *x* if the pair of figures is similar: - The ratio of corresponding sides will be equal. * *x/3 = 4/6* * *x* = (4 * 3) / 6 = **2** ### Analyze the following pair of similar triangles: - In the diagram, we see that triangle *ABC* is similar to triangle *GHE*. - The correct statement for "a" is [a] **corresponding sides of similar triangles are in proportion** - The correct statement for "b" is [b] **corresponding angles of similar triangles are congruent** ### Examine the triangles below: - **Original figure:** sides are 15, 20 * **New figure:** sides are 6, 8 * The ZOOM FACTOR (New/Original) for the for the above triangles is [a] **2/5** * The hypothenuse of the new figure is [b] **10** * The area of the new figure is [c] **24** ### Solve for _w_. - Triangle *NOP* is similar to triangle *XYZ*. - _w/12 = 3/7_ - _w_ = (3 * 12) / 7 = **5.14** (rounded to the nearest hundredth) ### Enlarge the following geometric shape by a zoom factor of 2 - **Original shape:** sides are 3, 4, 5, 6 * What is the perimeter of the new figure? [a] **36** * What is the area of the new figure? [b] **120** ### Determine if the two triangles are congruent. If they are, state the condition. - Two triangles are congruent if all corresponding sides and angles are equal. - The given triangles have two corresponding sides and a corresponding angle equal. - We do not have enough information to determine if the triangles are congruent. ### State what additional information is required in order to know that the triangles are congruent for the reason given. - **ASA:** Two angles and the included side are congruent ### Which diagram(s) show alternate interior angles? - Diagrams I, IV, V and VII show **alternate interior angles**. ### What is the length of *BI*? - Triangle *SML* is similar to Triangle *BIG*. - The ratio of corresponding sides will be equal. - *BI/16 = 42/12* - *BI* = (42 * 16) / 12 = **56 cm** ### Lindy gets nosebleeds whenever she is more than 300 feet above the ground. - What mathematical tool should Lindy use in order to calculate the height of the Statue of Liberty? [a] **Trigonometry** - What side of the right triangle should you be calculating? [b] **Opposite** - What is the approximated height of the Statue of Liberty? [c] **311 feet** - Should Lindy be able to climb without getting a nosebleed? [d] **Yes** ### Emir's little brother loves to go down the big slide at the neighborhood playground. - How long is the slide? - The slide forms the hypotenuse of a right triangle with height of 11 feet and angle of 40°. - We can use the sine function: *sin(40°) = 11/hypotenuse* - hypotenuse = 11 / *sin(40°)*= **17 feet** ### Find the missing side. Round to the nearest tenth. - *a^2 + b^2 = c^2* * *17^2 + x^2 = 20^2* * *x^2 = 20^2 - 17^2* * _x_ = sqrt(20^2 - 17^2) = **9.5** ### Solve for *x*. Round your answers to the hundredths place. (Two decimal places). - *cos(22°) = 17/x* * *x* = 17/ *cos(22°)* = **18.37** ### Find the missing angle and round to the nearest whole number. - *sin(angle) = 9/20* * angle = *arcsin(9/20)* = **26°** ### Find the missing side. Round to the nearest tenth. - *cos(59°) = *x*/14* * *x* = 14 * *cos(59°)* = **7.2**