Jane observed that a point looked like a dot. Which of the following set of objects represents a point?

Consider the line with points A, B, and C in that order, where B is the midpoint between A and C. Which of the following represents the ray that starts at point A and extends infinitely through point C?

Angles are formed by two intersecting lines. In the word L O V E, which of the following letters formed an angle?

A carpenter is designing a picture frame. The corners of the frame are made with different angles. One corner has a 90° angle. Another corner has a 150° angle. The third corner has a 45° angle. Which of the following correctly matches the angles with their classifications?

You are standing at a crossroad where two roads intersect each other. At this point, you are standing at the common vertex. What type of angle pair is formed by your view when you look straight ahead and then look to your right or left?

Sara is designing a picture frame. She wants the corners to be right angles, but she accidentally measures one corner as 92°. What is the measure of the other angle at that corner and what kind of angles are they if they’re supplementary?

At a road crossing, two straight roads intersect. One of the angles formed is 120°. The angle next to it forms a straight line with the 120° angle. What is the measure of the adjacent angle?

Which of the following is TRUE about pair of angles when two parallel lines are cut by a transversal?

Two parallel lines l1 and l2 are cut by a transversal t. At the intersection of t and l1, angle 1 measures 35°. What is the measure of the alternate interior angle of angle 1?

In the given diagram, lines AB and CD are parallel. A transversal line intersects these parallel lines. What is the measure of ∠x?

Czarina was asked to draw ray OB bisecting ∠AOC. Which of the following illustrations shows OB bisects ∠AOC?

If you are going to construct line JK with a segment bisector line VW where they intersect at •M, what could be the figure and explain the relationship of JM and MK

Ellaine is studying polygons for her exam; she noticed that some parts of a polygon have equal numbers. Which parts of the polygons are equal in number?

A road sign can be shaped like a polygon, such as a stop sign that has 8 sides and a convex polygon. Which statement correctly applies to this description?

During your mathematics class, your teacher gave you an assignment to draw three different types of convex polygons. Polygons should vary in the number of sides, and you need to make sure each one is convex, meaning all their interior angles must be less than 180 degrees and no vertices point inward. Which of the following will you draw?

Mr. Cole is designing a star shape where it has 10 points. He wants to know the measure of each interior angle of the star. (Note that the star can be thought of as regular decagon (10-sided polygon) with each angle formed by extending two adjacent sides). What is the measure of each interior angle of the star?

Sam is studying a regular polygon where the sum of each exterior angle and its adjacent interior angle is 180°. If each exterior angle measures 30°, how many sides does the polygon have?

In Math subject, Marie was asked by her teacher what formula she must apply in finding the measure of each interior angle of a regular polygon. She came up with the answer and presented it to her teacher. Which formula below should Marie apply?

Imagine you’re building a circular garden. You measure the distance across the garden through the center (diameter). You also measure the distance from the center of the garden to the edge (radius). Which of the following statements BEST describes the relationship between the diameter and the radius of your circular garden? Choose all that apply.

i. All radii of a circle are equal in length.

ii. The diameter is twice the measure of the radius.

iii. The circumference is the distance around the circle.

iv. The radius is half of the diameter.

Anton’s task given by her Geometry teacher is to construct OP and draw a diameter on that circle. He understands that there is consideration to be done in sketching a diameter. Which options below should Anton consider?

You are designing a circular flower bed inside a square lawn. To use the maximum possible area, which design should you create?

Geometric tools are instruments used in Math, Science, and Art to accurately draw, measure and construct geometric shapes, lines and angles. Which of the following instruments is essential for constructing a regular polygon using the classical geometric method?

Grade 7- Dahlia is asked to construct a regular hexagon using a compass and ruler. Why is it necessary that the compass opening is kept equal to the radius of the circle throughout the construction?

A student solves a problem and states: “The sum of interior angles of a polygon is $$1260^\circ$$ , so the polygon has $$9$$ sides.” Evaluate the student’s conclusion and choose the option that best justifies your decision.

BELVEDERE TOWN PARK. An urban planner is renovating the park at Belvedere Town. To represent different elements on a digital map, the planner uses basic geometric concepts: • Points represent light poles. • Lines represent straight walking paths. • Planes represent flat grassy fields. Based on the geometric properties of a line and a plane in space, is it possible for a line and plane to intersect at exactly two points?

STRAW FISH WALL HANGING. During Arts class, teacher Joanna asked her students to bring scissors, threads, straws, colored paper, and ruler. Marie noticed that these objects represent undefined terms in Geometry. Which of the following sets of objects represent a line?

A CUTE HOME. Angelo observed that some of their things at home represent an angle. He knows that an acute angle measures less than $$90^\circ$$ but greater than $$0^\circ$$ . Which of the following real-life objects typically features an acute angle?

i. corner of the television

ii. a partially opened door

iii. tips of the scissors

iv. the hands of an analog clock at 2:00

PEDESTRIAN BRIDGE. A structural engineering firm is auditing the safety of a newly constructed pedestrian bridge in Robinson’s GenTri. The city’s strict safety guidelines require that the angle of the main structural support must be obtuse to properly distribute weight during high-wind events. If the support forms an acute or right angle, it is deemed structurally unsound for this specific bridge design. During the audit, the lead engineer measures the internal angle of the support beam and finds it is exactly $$89.7^\circ$$ . Evaluate the safety of the bridge support based on the city's mandatory safety guidelines. Which of the following conclusions is most mathematically and professionally justified?

WHAT TIME IS IT? Using the clock as representation of different kinds of angles. What time will show an example of an obtuse angle? (Remember the angles measuring greater than $$90^\circ$$ and less than $$180^\circ$$ are called obtuse angle)

AJAR. Maria is opening the door. The door forms a $$30^\circ$$ angle with the wall when it is slightly open. She wants to open the door further so that the angle between the door and the wall becomes $$90^\circ$$ . How much more does Maria need to open the door? What type of angle does the door form?

PARKING AREA. A parking space or parking area is a location that is designated for parking a vehicle. It can be in a parking garage, in a parking lot or on a city street. The space may be delineated by road surface markings. On the right is the picture of a parking space. The design is composed of parallel and perpendicular lines. Why are parking lots designed to be like this?

TRIANGULAR GARDEN. A millionaire has donated a large amount of money to a local government unit for the construction of a triangular garden outside their building. One of the angles of the triangular garden is $$50^\circ$$ . What are the possible measurements of the two remaining angles and why?

THE THREE ARCHERS. The three archers were practicing shooting an arrow for the Olympics. The arrows shot by the three archers hit a tree as shown on the right. Arrows A and B are in parallel to the ground and arrow C cuts across the other two arrows. If m∠1 is 130°, which of the following statement is correct?

LEANING TOWER OF PISA. The Leaning Tower of Pisa is one of the most remarkable architectural structures from medieval Europe. This tower shows an example of a linear pair because of its formed angle on the sides. If one angle measures 87°, what is the measure of another angle and why?

RAILWAY TRACKS. Two railway tracks run parallel to each other. A pedestrian crossing cuts across the tracks at an angle, forming intersections with each track. A student notices the angles formed where the crossing meets each track. Which statement best explains the relationship between the angles formed on the same side of the crossing at each track?

STREET-WISE. A city architect is designing a pedestrian crossing pattern. Two parallel streets, Street A and Street B, are crossed by a straight pedestrian path. At the point where the path crosses Street B, the angle between the path and the street is 65°, as shown on the right. Which of the following is the measure of the corresponding angle formed where the path crosses Street A?

DIVIDE ME EQUALLY. A landscape engineer is constructing a triangular garden at a city park. At one corner of the garden, the angle between two walkways is 72°. How will the engineer apply the angle bisector theorem?

POLYGON MUSEUM. Grade 7 students of TNTS conduct an educational trip in a museum located at Manila. During their trip inside the museum, they encounter different paintings, portraits, antique objects, mosaic, and artwork created by various well-known people in the country. Some of these are the following: Which of the following statements correctly classifies each figure as convex or non-convex?

RUN FOR YOUR LIFE. In a rectangular basketball court ABCD, a player was asked by his coach to run from vertex A to any vertices making a line diagonally. Which of the following diagonals may the player run to?

ARCHITECTURAL DESIGN REVIEW. An architect designs the floor plan of a small art gallery in the shape of a polygon. From the blueprint, the floor plan has: five sides of different lengths and one interior angle greater than 180°, forming an inward corner. During the design review, a committee member states: “This floor plan is a convex pentagon because it has five sides”. How should the committee evaluate this statement?

AT MAPLE GROVE PARK VILLAGE. At Maple Grove Park Village in General Trias, Cavite, many of the areas are designed using geometric shapes, particularly convex polygons, to create smooth pathways, safe gathering areas, and visually appealing layouts. To ensure that walkways connect properly and that decks and garden borders align neatly, the planners review basic geometric properties of polygons. Which statement correctly states the relationship between an exterior angle and its adjacent interior angle of a convex polygon?

REGULAR HEXAGONAL TABLE. The canteen of Tanza National Trade School has a regular hexagonal table. The school wants to place chairs at each vertex so that students can sit around it. If each exterior angle of the table is 60°, which statement correctly applies to the relationship between interior and exterior angles?

VERTICAL ANGLE THEOREM. Madie tries to intersect two lines. Four angles were formed such as ∠1, ∠2, ∠3, and ∠4. The Vertical Angle Theorem states that if two lines cross at a single point, two pairs of congruent angles are formed. Refer to the figure at the right, if ∠1 measures 25°, what is the measure of ∠3 and why?

THE SPRINKLER SYSTEM. Refer to the illustration on the right. Which of the following is the name of the circle representing the area of lawn watered by the sprinkler?

THE CLOCK FACE. A clock has a circular face with a radius of $$6$$ inches. A designer needs to know the diameter of the clock face to create the outer casing. Which statement correctly shows the relationship between the clock's radius and diameter?

EQUILATERAL TRIANGLE GARDEN. Maria wants to create a small triangular garden in her backyard. She wants the garden to be an equilateral triangle. What would be the correct illustration of the garden if she follows the steps in constructing a regular triangle?

TILE PATERN. Gina, a designer student, is learning how to construct regular polygons for a decorative tile pattern. She draws a circle and plans to construct a regular pentagon inside it using a compass and ruler. Which explanation best shows that the student understands how a regular pentagon can be constructed using a circle?

POLYGON-SHAPED GARDEN. A landscaping company is designing a regular polygon-shaped garden. Each corner of the garden has the same interior angle so that fence panels of equal length can be used. The design plan shows that each interior angle of the garden is $$140^\circ$$ . Using this information, how many sides will the garden have?

WALKING PATH. A city engineers plans to design a regular polygon-shaped walking path. The total sum of interior angles must be $$720^\circ$$ . Which design plan correctly determines the shape?