The post Multiplication of Integers (Practice Quiz) appeared first on GeoGebra Institute of Manila.

]]>1.) Use the sliders to adjust the minimum and maximum values of the factors.

2.) Type your answers in the text boxes.

3.) Click on the “Check Answers” command button to check your answer.

4.) Click the “New Set” command button to generate new sets of factors.

The post Multiplication of Integers (Practice Quiz) appeared first on GeoGebra Institute of Manila.

]]>The post Subtraction of Integers (Practice Quiz) appeared first on GeoGebra Institute of Manila.

]]>1.) Use the sliders to adjust the minimum and maximum values of the minuends/subtrahends.

2.) Type your answers in the text boxes.

3.) Click on the “Check Answers” command button to check your answer.

4.) Click the “New Set” command button to generate new sets of minuends/subtrahends.

The post Subtraction of Integers (Practice Quiz) appeared first on GeoGebra Institute of Manila.

]]>The post Slope and y-intercept appeared first on GeoGebra Institute of Manila.

]]>**Questions**

- How does the value of
*m*and*b*affect the graph of y = mx + b? - .Without using GeoGebra, explain and justify what should be the values of
*m*and*b*so that the graph passes through- Quadrants I, II, and III
- Quadrants I, II, and IV
- Quadrants I and III only
- Quadrants III and IV only

- Explain and justify why
*m*> 0 when the graph slants to the right.*m*< 0 when the graph slants to the left.*m*= 0 when the graph is horizontal.

The post Slope and y-intercept appeared first on GeoGebra Institute of Manila.

]]>The post Addition of Integers (Practice Quiz) appeared first on GeoGebra Institute of Manila.

]]>1.) Use the sliders to adjust the minimum and maximum values of the addends.

2.) Type your answers in the text boxes.

3.) Click on the “Check Answers” command button to check your answer.

4.) Click the “New Set” command button to generate a new sets of addends.

The post Addition of Integers (Practice Quiz) appeared first on GeoGebra Institute of Manila.

]]>The post The Midline Theorem appeared first on GeoGebra Institute of Manila.

]]>1.) What did you observe in your investigation?

2.) What do your observations about the measures of the angles mean? How do they relate to the properties of the segments?

3.) What did you observe about the lengths of segment DE and segment BC? Was this observation always true?

4.) Based on the discussion, make conjectures about the relationship between segment AB and segment BC.

The post The Midline Theorem appeared first on GeoGebra Institute of Manila.

]]>The post The Pantograph appeared first on GeoGebra Institute of Manila.

]]>The applet above demonstrates how the pantograph works. Move the blue point (hinge) and draw any shape.

Questions:

1.) What do you observe?

2.) What is the relationship between the blue figure and red figure?

3.) Justify your answer in 2.

4.) Prove that the relationship in 2 always holds.

The post The Pantograph appeared first on GeoGebra Institute of Manila.

]]>The post Pythagorean Theorem appeared first on GeoGebra Institute of Manila.

]]>1) What type of quadrilateral is the white region? Justify your answer.

2) What is the area of the quadrilateral in (1)?

3) Move slider *R* to the extreme right to show slider *T*. Then, move slider *T* to the extreme right. What type/s of quadrilateral are the two white regions? Justify your answer.

4.) What are the areas of the quadrilaterals in (3)?

5.) How does the area of the quadrilateral in (1) relate to the areas of the quadrilaterals in (3)?

6.) What equation can we form from the relationship in (4) in terms of *a*, *b*, and *c*?

The post Pythagorean Theorem appeared first on GeoGebra Institute of Manila.

]]>The post Copying a Segment appeared first on GeoGebra Institute of Manila.

]]>The post Copying a Segment appeared first on GeoGebra Institute of Manila.

]]>The post Task 5 – Distance from Point of Similarity appeared first on GeoGebra Institute of Manila.

]]>1.) What is the ratio of the lengths of the corresponding sides?

2.) What is the ratio of the distance from point P to the corresponding vertices?

3.) What conjecture can you make from your answer in 1 and 2? Verify your conjectures by drawing a different pair of similar triangles.

**Explanation **

The ratio of the corresponding sides of two similar triangles is the same as the ratio of the distance of their corresponding vertices to the center of similarity. The ratio of the corresponding sides of two similar triangles is the same as the ratio of the distance of their corresponding vertices. In the figure above, ∆ABC ~ ∆A’B’C’ so

and

The post Task 5 – Distance from Point of Similarity appeared first on GeoGebra Institute of Manila.

]]>The post Task 4 – Point of Similarity appeared first on GeoGebra Institute of Manila.

]]>

**Questions**

1.) Are the two triangles similar? Why?

2.) What is the ratio of the lengths of their corresponding sides?

3.) Use the **Line** tool to connect the corresponding vertices of the two triangles. Did your observations in **Task 2** and **Task 3** hold?

4.) Make a conjecture about the lines connecting the corresponding vertices of similar triangles.

[toggle title=’Explanation’ title_font_size=’14px’]If two triangles are similar and their corresponding sides are parallel, then the line connecting their corresponding vertices will intersect at a point. This point is called the **center of similarity** or point of similarity.

In Task 3, and their corresponding sides are parallel. The three lines connecting the corresponding vertices intersect point as shown above. In Task 4, , but their corresponding sides are not parallel, so the three lines connecting their corresponding vertices do not intersect at a point.

[/toggle]

**Task 5 >>**

The post Task 4 – Point of Similarity appeared first on GeoGebra Institute of Manila.

]]>